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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 7056cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7056.a2 | 7056cd1 | \([0, 0, 0, 17493, -18991910]\) | \(4913/1296\) | \(-156161811398197248\) | \([2]\) | \(86016\) | \(1.9783\) | \(\Gamma_0(N)\)-optimal |
| 7056.a1 | 7056cd2 | \([0, 0, 0, -970347, -357821030]\) | \(838561807/26244\) | \(3162276680813494272\) | \([2]\) | \(172032\) | \(2.3249\) |
Rank
sage: E.rank()
The elliptic curves in class 7056cd have rank \(0\).
Complex multiplication
The elliptic curves in class 7056cd do not have complex multiplication.Modular form 7056.2.a.cd
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
