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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 5292.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5292.b1 | 5292g2 | \([0, 0, 0, -5439, -172186]\) | \(-2431344/343\) | \(-2510317184256\) | \([]\) | \(10368\) | \(1.1105\) | |
| 5292.b2 | 5292g1 | \([0, 0, 0, 441, 686]\) | \(11664/7\) | \(-5692329216\) | \([]\) | \(3456\) | \(0.56114\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5292.b have rank \(1\).
Complex multiplication
The elliptic curves in class 5292.b do not have complex multiplication.Modular form 5292.2.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.
