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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 397800.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
397800.x1 | 397800x1 | \([0, 0, 0, -3214875, -2210980250]\) | \(315042014258500/1262881737\) | \(14730252580368000000\) | \([2]\) | \(8847360\) | \(2.5346\) | \(\Gamma_0(N)\)-optimal |
397800.x2 | 397800x2 | \([0, 0, 0, -1693875, -4308439250]\) | \(-23040414103250/330419182041\) | \(-7708018678652448000000\) | \([2]\) | \(17694720\) | \(2.8812\) |
Rank
sage: E.rank()
The elliptic curves in class 397800.x have rank \(1\).
Complex multiplication
The elliptic curves in class 397800.x do not have complex multiplication.Modular form 397800.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.