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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3700.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3700.b1 | 3700f1 | \([0, 1, 0, -708, 7588]\) | \(-393040/37\) | \(-3700000000\) | \([3]\) | \(2160\) | \(0.57794\) | \(\Gamma_0(N)\)-optimal |
| 3700.b2 | 3700f2 | \([0, 1, 0, 4292, -2412]\) | \(87418160/50653\) | \(-5065300000000\) | \([]\) | \(6480\) | \(1.1272\) |
Rank
sage: E.rank()
The elliptic curves in class 3700.b have rank \(0\).
Complex multiplication
The elliptic curves in class 3700.b do not have complex multiplication.Modular form 3700.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
