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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 249900bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 249900.bl1 | 249900bl1 | \([0, -1, 0, -413233, 102283462]\) | \(265327034368/297381\) | \(8746644317250000\) | \([2]\) | \(2211840\) | \(1.9730\) | \(\Gamma_0(N)\)-optimal |
| 249900.bl2 | 249900bl2 | \([0, -1, 0, -309108, 154970712]\) | \(-6940769488/18000297\) | \(-8470867767012000000\) | \([2]\) | \(4423680\) | \(2.3196\) |
Rank
sage: E.rank()
The elliptic curves in class 249900bl have rank \(1\).
Complex multiplication
The elliptic curves in class 249900bl do not have complex multiplication.Modular form 249900.2.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 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.
