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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 3525.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3525.d1 | 3525b3 | \([1, 1, 1, -26938, -1296094]\) | \(138356873478361/34423828125\) | \(537872314453125\) | \([2]\) | \(10368\) | \(1.5368\) | |
| 3525.d2 | 3525b2 | \([1, 1, 1, -9313, 325406]\) | \(5717095008841/310640625\) | \(4853759765625\) | \([2, 2]\) | \(5184\) | \(1.1902\) | |
| 3525.d3 | 3525b1 | \([1, 1, 1, -9188, 335156]\) | \(5489965305721/17625\) | \(275390625\) | \([4]\) | \(2592\) | \(0.84361\) | \(\Gamma_0(N)\)-optimal |
| 3525.d4 | 3525b4 | \([1, 1, 1, 6312, 1325406]\) | \(1779919481159/49406770125\) | \(-771980783203125\) | \([2]\) | \(10368\) | \(1.5368\) |
Rank
sage: E.rank()
The elliptic curves in class 3525.d have rank \(1\).
Complex multiplication
The elliptic curves in class 3525.d do not have complex multiplication.Modular form 3525.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
