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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 32340.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32340.bl1 | 32340bj2 | \([0, 1, 0, -1738340, 714049188]\) | \(19288565375865424/3837216796875\) | \(115569848047500000000\) | \([2]\) | \(829440\) | \(2.5660\) | |
| 32340.bl2 | 32340bj1 | \([0, 1, 0, 226315, 66498900]\) | \(681010157060096/1406657896875\) | \(-2647870318551150000\) | \([2]\) | \(414720\) | \(2.2194\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32340.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 32340.bl do not have complex multiplication.Modular form 32340.2.a.bl
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.
