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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 436425z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
436425.z1 | 436425z1 | \([0, -1, 1, -12343, -549597]\) | \(-56197120/3267\) | \(-12090831234075\) | \([]\) | \(855360\) | \(1.2665\) | \(\Gamma_0(N)\)-optimal* |
436425.z2 | 436425z2 | \([0, -1, 1, 67007, -1001892]\) | \(8990228480/5314683\) | \(-19669095566454675\) | \([]\) | \(2566080\) | \(1.8158\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 436425z have rank \(1\).
Complex multiplication
The elliptic curves in class 436425z do not have complex multiplication.Modular form 436425.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.