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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 7605.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7605.d1 | 7605n2 | \([1, -1, 1, -2625278, -1636478944]\) | \(258840217117/18225\) | \(140891643782162325\) | \([2]\) | \(119808\) | \(2.3433\) | |
| 7605.d2 | 7605n1 | \([1, -1, 1, -153653, -28934044]\) | \(-51895117/16875\) | \(-130455225724224375\) | \([2]\) | \(59904\) | \(1.9967\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7605.d have rank \(1\).
Complex multiplication
The elliptic curves in class 7605.d do not have complex multiplication.Modular form 7605.2.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.
