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SageMath
E = EllipticCurve("ds1")
E.isogeny_class()
Elliptic curves in class 127296ds
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 127296.t1 | 127296ds1 | \([0, 0, 0, -36336, 1912376]\) | \(7107347955712/1996623837\) | \(1490471707825152\) | \([2]\) | \(442368\) | \(1.6185\) | \(\Gamma_0(N)\)-optimal |
| 127296.t2 | 127296ds2 | \([0, 0, 0, 94884, 12567440]\) | \(7909612346288/10289870721\) | \(-122901557339897856\) | \([2]\) | \(884736\) | \(1.9651\) |
Rank
sage: E.rank()
The elliptic curves in class 127296ds have rank \(1\).
Complex multiplication
The elliptic curves in class 127296ds do not have complex multiplication.Modular form 127296.2.a.ds
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 Cremona 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 Cremona labels.
