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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 141960.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141960.r1 | 141960ci6 | \([0, -1, 0, -1771176, -906668244]\) | \(62161150998242/1607445\) | \(15890083825674240\) | \([2]\) | \(2359296\) | \(2.2154\) | |
| 141960.r2 | 141960ci4 | \([0, -1, 0, -114976, -12982724]\) | \(34008619684/4862025\) | \(24031299612902400\) | \([2, 2]\) | \(1179648\) | \(1.8688\) | |
| 141960.r3 | 141960ci2 | \([0, -1, 0, -30476, 1855476]\) | \(2533446736/275625\) | \(340579643040000\) | \([2, 2]\) | \(589824\) | \(1.5222\) | |
| 141960.r4 | 141960ci1 | \([0, -1, 0, -29631, 1973100]\) | \(37256083456/525\) | \(40545195600\) | \([2]\) | \(294912\) | \(1.1757\) | \(\Gamma_0(N)\)-optimal |
| 141960.r5 | 141960ci3 | \([0, -1, 0, 40504, 9152220]\) | \(1486779836/8203125\) | \(-40545195600000000\) | \([2]\) | \(1179648\) | \(1.8688\) | |
| 141960.r6 | 141960ci5 | \([0, -1, 0, 189224, -70294004]\) | \(75798394558/259416045\) | \(-2564406683136829440\) | \([2]\) | \(2359296\) | \(2.2154\) |
Rank
sage: E.rank()
The elliptic curves in class 141960.r have rank \(0\).
Complex multiplication
The elliptic curves in class 141960.r do not have complex multiplication.Modular form 141960.2.a.r
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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
