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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 348480.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.q1 | 348480q1 | \([0, 0, 0, -95403, -11339152]\) | \(1546408574144/455625\) | \(28293918840000\) | \([2]\) | \(1474560\) | \(1.5600\) | \(\Gamma_0(N)\)-optimal |
| 348480.q2 | 348480q2 | \([0, 0, 0, -83028, -14388352]\) | \(-15926924096/13286025\) | \(-52803243095961600\) | \([2]\) | \(2949120\) | \(1.9066\) |
Rank
sage: E.rank()
The elliptic curves in class 348480.q have rank \(1\).
Complex multiplication
The elliptic curves in class 348480.q do not have complex multiplication.Modular form 348480.2.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.
