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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 9240u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9240.m5 | 9240u1 | \([0, -1, 0, -1055, 12072]\) | \(8124052043776/992578125\) | \(15881250000\) | \([4]\) | \(8192\) | \(0.68764\) | \(\Gamma_0(N)\)-optimal |
| 9240.m4 | 9240u2 | \([0, -1, 0, -4180, -90428]\) | \(31558509702736/4035425625\) | \(1033068960000\) | \([2, 4]\) | \(16384\) | \(1.0342\) | |
| 9240.m2 | 9240u3 | \([0, -1, 0, -64680, -6309828]\) | \(29224056825643684/588305025\) | \(602424345600\) | \([2, 2]\) | \(32768\) | \(1.3808\) | |
| 9240.m6 | 9240u4 | \([0, -1, 0, 6320, -481028]\) | \(27258770992316/112538412525\) | \(-115239334425600\) | \([4]\) | \(32768\) | \(1.3808\) | |
| 9240.m1 | 9240u5 | \([0, -1, 0, -1034880, -404867988]\) | \(59850000883110493442/24255\) | \(49674240\) | \([2]\) | \(65536\) | \(1.7274\) | |
| 9240.m3 | 9240u6 | \([0, -1, 0, -62480, -6761268]\) | \(-13171152353214242/2080257264855\) | \(-4260366878423040\) | \([2]\) | \(65536\) | \(1.7274\) |
Rank
sage: E.rank()
The elliptic curves in class 9240u have rank \(0\).
Complex multiplication
The elliptic curves in class 9240u do not have complex multiplication.Modular form 9240.2.a.u
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
