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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 377520bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.bu7 | 377520bu1 | \([0, -1, 0, -22109160, -38268896400]\) | \(164711681450297281/8097103872000\) | \(58755127019864850432000\) | \([2]\) | \(39813120\) | \(3.1283\) | \(\Gamma_0(N)\)-optimal |
| 377520.bu6 | 377520bu2 | \([0, -1, 0, -61758440, 137393273712]\) | \(3590017885052913601/954068544000000\) | \(6923020795400945664000000\) | \([2, 2]\) | \(79626240\) | \(3.4749\) | |
| 377520.bu3 | 377520bu3 | \([0, -1, 0, -1769155560, -28641001768080]\) | \(84392862605474684114881/11228954880\) | \(81480820884142817280\) | \([2]\) | \(119439360\) | \(3.6776\) | |
| 377520.bu5 | 377520bu4 | \([0, -1, 0, -913598440, 10627973241712]\) | \(11621808143080380273601/1335706803288000\) | \(9692307784252180758528000\) | \([2]\) | \(159252480\) | \(3.8214\) | |
| 377520.bu8 | 377520bu5 | \([0, -1, 0, 155693080, 888557804400]\) | \(57519563401957999679/80296734375000000\) | \(-582658306236864000000000000\) | \([2]\) | \(159252480\) | \(3.8214\) | |
| 377520.bu2 | 377520bu6 | \([0, -1, 0, -1769310440, -28635736095888]\) | \(84415028961834287121601/30783551683856400\) | \(223375112620459326834278400\) | \([2, 2]\) | \(238878720\) | \(4.0242\) | |
| 377520.bu1 | 377520bu7 | \([0, -1, 0, -2026992040, -19747988493968]\) | \(126929854754212758768001/50235797102795981820\) | \(364526710584223139221590097920\) | \([2]\) | \(477757440\) | \(4.3708\) | |
| 377520.bu4 | 377520bu8 | \([0, -1, 0, -1514106920, -37186483155600]\) | \(-52902632853833942200321/51713453577420277500\) | \(-375249049735447528358615040000\) | \([2]\) | \(477757440\) | \(4.3708\) |
Rank
sage: E.rank()
The elliptic curves in class 377520bu have rank \(0\).
Complex multiplication
The elliptic curves in class 377520bu do not have complex multiplication.Modular form 377520.2.a.bu
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
