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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 85680.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85680.d1 | 85680dt1 | \([0, 0, 0, -119388, 9920563]\) | \(16134601070166016/5692058203125\) | \(66392166881250000\) | \([2]\) | \(737280\) | \(1.9291\) | \(\Gamma_0(N)\)-optimal |
| 85680.d2 | 85680dt2 | \([0, 0, 0, 358737, 69494938]\) | \(27358024514264624/27011695685625\) | \(-5041030695634080000\) | \([2]\) | \(1474560\) | \(2.2757\) |
Rank
sage: E.rank()
The elliptic curves in class 85680.d have rank \(1\).
Complex multiplication
The elliptic curves in class 85680.d do not have complex multiplication.Modular form 85680.2.a.d
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.
