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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3726.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3726.b1 | 3726b2 | \([1, -1, 0, -260376, -51085504]\) | \(-33060921612804657/8875147264\) | \(-524068570791936\) | \([]\) | \(34560\) | \(1.8080\) | |
3726.b2 | 3726b1 | \([1, -1, 0, 1479, -252307]\) | \(490609013103/37897187584\) | \(-27627049748736\) | \([3]\) | \(11520\) | \(1.2587\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3726.b have rank \(0\).
Complex multiplication
The elliptic curves in class 3726.b do not have complex multiplication.Modular form 3726.2.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.