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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 13328q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13328.q2 | 13328q1 | \([0, 0, 0, 1421, 10290]\) | \(658503/476\) | \(-229379784704\) | \([2]\) | \(9216\) | \(0.86825\) | \(\Gamma_0(N)\)-optimal |
13328.q1 | 13328q2 | \([0, 0, 0, -6419, 87122]\) | \(60698457/28322\) | \(13648097189888\) | \([2]\) | \(18432\) | \(1.2148\) |
Rank
sage: E.rank()
The elliptic curves in class 13328q have rank \(0\).
Complex multiplication
The elliptic curves in class 13328q do not have complex multiplication.Modular form 13328.2.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.