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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 9240.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9240.l1 | 9240h4 | \([0, -1, 0, -8240, 290652]\) | \(60430765429444/2525985\) | \(2586608640\) | \([2]\) | \(12288\) | \(0.88674\) | |
| 9240.l2 | 9240h3 | \([0, -1, 0, -2520, -44100]\) | \(1729010797924/148561875\) | \(152127360000\) | \([2]\) | \(12288\) | \(0.88674\) | |
| 9240.l3 | 9240h2 | \([0, -1, 0, -540, 4212]\) | \(68150496976/12006225\) | \(3073593600\) | \([2, 2]\) | \(6144\) | \(0.54016\) | |
| 9240.l4 | 9240h1 | \([0, -1, 0, 65, 340]\) | \(1869154304/4611915\) | \(-73790640\) | \([4]\) | \(3072\) | \(0.19359\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9240.l have rank \(1\).
Complex multiplication
The elliptic curves in class 9240.l do not have complex multiplication.Modular form 9240.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
