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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 9408.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9408.q1 | 9408bp2 | \([0, -1, 0, -442241, 117590817]\) | \(-6329617441/279936\) | \(-423041520824745984\) | \([]\) | \(112896\) | \(2.1472\) | |
| 9408.q2 | 9408bp1 | \([0, -1, 0, -3201, -159711]\) | \(-2401/6\) | \(-9067247960064\) | \([]\) | \(16128\) | \(1.1742\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9408.q have rank \(0\).
Complex multiplication
The elliptic curves in class 9408.q do not have complex multiplication.Modular form 9408.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
