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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 193200.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193200.q1 | 193200eo1 | \([0, -1, 0, -2066008, 1142870512]\) | \(15238420194810961/12619514880\) | \(807648952320000000\) | \([2]\) | \(3870720\) | \(2.3644\) | \(\Gamma_0(N)\)-optimal |
| 193200.q2 | 193200eo2 | \([0, -1, 0, -1618008, 1651798512]\) | \(-7319577278195281/14169067365600\) | \(-906820311398400000000\) | \([2]\) | \(7741440\) | \(2.7110\) |
Rank
sage: E.rank()
The elliptic curves in class 193200.q have rank \(1\).
Complex multiplication
The elliptic curves in class 193200.q do not have complex multiplication.Modular form 193200.2.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.
