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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 190575.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.bd1 | 190575bs2 | \([1, -1, 1, -58765730, 17763644022]\) | \(835630707059/478515625\) | \(12852210917695770263671875\) | \([2]\) | \(30412800\) | \(3.5077\) | |
| 190575.bd2 | 190575bs1 | \([1, -1, 1, 14605645, 2208912522]\) | \(12829337821/7503125\) | \(-201522667189469677734375\) | \([2]\) | \(15206400\) | \(3.1611\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190575.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 190575.bd do not have complex multiplication.Modular form 190575.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
