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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 95370.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95370.v1 | 95370v2 | \([1, 1, 0, -10650667, -13778409731]\) | \(-66277326463129/2299968000\) | \(-4636721459227885632000\) | \([]\) | \(10707552\) | \(2.9304\) | |
95370.v2 | 95370v1 | \([1, 1, 0, 624668, -65347304]\) | \(13371532631/8660520\) | \(-17459555494716573480\) | \([]\) | \(3569184\) | \(2.3811\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95370.v have rank \(1\).
Complex multiplication
The elliptic curves in class 95370.v do not have complex multiplication.Modular form 95370.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.