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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 207025q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
207025.q2 | 207025q1 | \([1, 0, 0, -1128, 11647]\) | \(4913\) | \(32309356625\) | \([2]\) | \(147456\) | \(0.73218\) | \(\Gamma_0(N)\)-optimal |
207025.q1 | 207025q2 | \([1, 0, 0, -17053, 855672]\) | \(16974593\) | \(32309356625\) | \([2]\) | \(294912\) | \(1.0788\) |
Rank
sage: E.rank()
The elliptic curves in class 207025q have rank \(2\).
Complex multiplication
The elliptic curves in class 207025q do not have complex multiplication.Modular form 207025.2.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.