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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 79350q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79350.l1 | 79350q1 | \([1, 1, 0, -505, -4175]\) | \(9393931/972\) | \(1478290500\) | \([2]\) | \(53760\) | \(0.49481\) | \(\Gamma_0(N)\)-optimal |
79350.l2 | 79350q2 | \([1, 1, 0, 645, -19125]\) | \(19465109/118098\) | \(-179612295750\) | \([2]\) | \(107520\) | \(0.84139\) |
Rank
sage: E.rank()
The elliptic curves in class 79350q have rank \(1\).
Complex multiplication
The elliptic curves in class 79350q do not have complex multiplication.Modular form 79350.2.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 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.