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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 422331q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422331.q2 | 422331q1 | \([1, 1, 1, 78497, 8729300]\) | \(42875/51\) | \(-63628046083437927\) | \([2]\) | \(2875392\) | \(1.9106\) | \(\Gamma_0(N)\)-optimal* |
422331.q1 | 422331q2 | \([1, 1, 1, -459768, 82794564]\) | \(8615125/2601\) | \(3245030350255334277\) | \([2]\) | \(5750784\) | \(2.2571\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 422331q have rank \(1\).
Complex multiplication
The elliptic curves in class 422331q do not have complex multiplication.Modular form 422331.2.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.