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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 71630.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
71630.v1 | 71630x2 | \([1, -1, 1, -6564370452, -204561760368501]\) | \(31282608380024362517498521417844241/25809317141410280453312834380\) | \(25809317141410280453312834380\) | \([]\) | \(183782144\) | \(4.3803\) | |
71630.v2 | 71630x1 | \([1, -1, 1, -265716552, 1667217712779]\) | \(2074815747201021028933709986641/5607507702833920000000\) | \(5607507702833920000000\) | \([7]\) | \(26254592\) | \(3.4073\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 71630.v have rank \(1\).
Complex multiplication
The elliptic curves in class 71630.v do not have complex multiplication.Modular form 71630.2.a.v
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 LMFDB 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 LMFDB labels.