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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 129430n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129430.s2 | 129430n1 | \([1, 1, 1, -5311291, 39274592713]\) | \(-2621279152968841/103908474880000\) | \(-656843193584376709120000\) | \([2]\) | \(22353408\) | \(3.2503\) | \(\Gamma_0(N)\)-optimal |
129430.s1 | 129430n2 | \([1, 1, 1, -208849211, 1155232300489]\) | \(159371806517831988361/1011781400000000\) | \(6395837555625488600000000\) | \([2]\) | \(44706816\) | \(3.5969\) |
Rank
sage: E.rank()
The elliptic curves in class 129430n have rank \(0\).
Complex multiplication
The elliptic curves in class 129430n do not have complex multiplication.Modular form 129430.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.