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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 41650.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41650.bd1 | 41650z1 | \([1, 1, 0, -450825, -116710075]\) | \(-137810063865625/17608192\) | \(-1294741362880000\) | \([]\) | \(497664\) | \(1.9213\) | \(\Gamma_0(N)\)-optimal |
| 41650.bd2 | 41650z2 | \([1, 1, 0, 69800, -364881600]\) | \(511460384375/782623571968\) | \(-57546800386539520000\) | \([]\) | \(1492992\) | \(2.4706\) |
Rank
sage: E.rank()
The elliptic curves in class 41650.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 41650.bd do not have complex multiplication.Modular form 41650.2.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 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.
