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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 7400.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7400.b1 | 7400j1 | \([0, 1, 0, -1208, 9088]\) | \(97556/37\) | \(74000000000\) | \([2]\) | \(7040\) | \(0.78504\) | \(\Gamma_0(N)\)-optimal |
| 7400.b2 | 7400j2 | \([0, 1, 0, 3792, 69088]\) | \(1507142/1369\) | \(-5476000000000\) | \([2]\) | \(14080\) | \(1.1316\) |
Rank
sage: E.rank()
The elliptic curves in class 7400.b have rank \(1\).
Complex multiplication
The elliptic curves in class 7400.b do not have complex multiplication.Modular form 7400.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
