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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 465460b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 465460.b1 | 465460b1 | \([0, 0, 0, -38332, 2887221]\) | \(151732224/85\) | \(3489387916240\) | \([2]\) | \(1244160\) | \(1.3539\) | \(\Gamma_0(N)\)-optimal |
| 465460.b2 | 465460b2 | \([0, 0, 0, -31487, 3950934]\) | \(-5256144/7225\) | \(-4745567566086400\) | \([2]\) | \(2488320\) | \(1.7005\) |
Rank
sage: E.rank()
The elliptic curves in class 465460b have rank \(1\).
Complex multiplication
The elliptic curves in class 465460b do not have complex multiplication.Modular form 465460.2.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 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.
