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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 358662y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
358662.y2 | 358662y1 | \([1, 0, 0, -878680, -319279552]\) | \(-506814405937489/4048994304\) | \(-599396471348576256\) | \([]\) | \(6286896\) | \(2.2392\) | \(\Gamma_0(N)\)-optimal |
358662.y1 | 358662y2 | \([1, 0, 0, -3767020, 31230058268]\) | \(-39934705050538129/2823126576537804\) | \(-417924052517300357247756\) | \([]\) | \(44008272\) | \(3.2122\) |
Rank
sage: E.rank()
The elliptic curves in class 358662y have rank \(0\).
Complex multiplication
The elliptic curves in class 358662y do not have complex multiplication.Modular form 358662.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.