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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 129430i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129430.e2 | 129430i1 | \([1, 1, 0, 2189178, 1026446356]\) | \(183550636104191/178095680000\) | \(-1125807450738528320000\) | \([]\) | \(6386688\) | \(2.7264\) | \(\Gamma_0(N)\)-optimal |
129430.e1 | 129430i2 | \([1, 1, 0, -51875582, 145247691964]\) | \(-2442316470222480769/28806640625000\) | \(-182097233612697265625000\) | \([]\) | \(19160064\) | \(3.2758\) |
Rank
sage: E.rank()
The elliptic curves in class 129430i have rank \(1\).
Complex multiplication
The elliptic curves in class 129430i do not have complex multiplication.Modular form 129430.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.