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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 53130.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53130.e1 | 53130d2 | \([1, 1, 0, -15624758, -23776589538]\) | \(421855440489788824984301929/42106031439084978750\) | \(42106031439084978750\) | \([2]\) | \(4362240\) | \(2.7999\) | |
53130.e2 | 53130d1 | \([1, 1, 0, -902688, -430330932]\) | \(-81346237678730525904649/32784643555577228700\) | \(-32784643555577228700\) | \([2]\) | \(2181120\) | \(2.4533\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53130.e have rank \(0\).
Complex multiplication
The elliptic curves in class 53130.e do not have complex multiplication.Modular form 53130.2.a.e
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.