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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 414736y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414736.y2 | 414736y1 | \([0, 0, 0, -3395651, -11209432766]\) | \(-60698457/725788\) | \(-51775581778940044361728\) | \([2]\) | \(29196288\) | \(3.0403\) | \(\Gamma_0(N)\)-optimal* |
414736.y1 | 414736y2 | \([0, 0, 0, -98784931, -376722075870]\) | \(1494447319737/5411854\) | \(386065751090792069914624\) | \([2]\) | \(58392576\) | \(3.3869\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414736y have rank \(0\).
Complex multiplication
The elliptic curves in class 414736y do not have complex multiplication.Modular form 414736.2.a.y
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.