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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 33488.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33488.q1 | 33488z2 | \([0, 0, 0, -335, -198]\) | \(16241202000/9332687\) | \(2389167872\) | \([2]\) | \(11520\) | \(0.48914\) | |
| 33488.q2 | 33488z1 | \([0, 0, 0, -220, 1251]\) | \(73598976000/336973\) | \(5391568\) | \([2]\) | \(5760\) | \(0.14257\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33488.q have rank \(0\).
Complex multiplication
The elliptic curves in class 33488.q do not have complex multiplication.Modular form 33488.2.a.q
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.
