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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 250470bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 250470.bd2 | 250470bd1 | \([1, -1, 0, -24804720, -3264603180800]\) | \(-1306902141891515161/3564268498800000000\) | \(-4603138599115914937200000000\) | \([2]\) | \(193536000\) | \(3.9870\) | \(\Gamma_0(N)\)-optimal |
| 250470.bd1 | 250470bd2 | \([1, -1, 0, -3454370640, -77165575538144]\) | \(3529773792266261468365081/50841342773437500000\) | \(65659965692844155273437500000\) | \([2]\) | \(387072000\) | \(4.3336\) |
Rank
sage: E.rank()
The elliptic curves in class 250470bd have rank \(0\).
Complex multiplication
The elliptic curves in class 250470bd do not have complex multiplication.Modular form 250470.2.a.bd
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.
