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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 24990n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24990.p2 | 24990n1 | \([1, 1, 0, 1683, -1859031]\) | \(1535602031153/4356914062500\) | \(-1494421523437500\) | \([2]\) | \(122880\) | \(1.5907\) | \(\Gamma_0(N)\)-optimal |
24990.p1 | 24990n2 | \([1, 1, 0, -217067, -38215281]\) | \(3297722675058468847/77753139806250\) | \(26669326953543750\) | \([2]\) | \(245760\) | \(1.9372\) |
Rank
sage: E.rank()
The elliptic curves in class 24990n have rank \(1\).
Complex multiplication
The elliptic curves in class 24990n do not have complex multiplication.Modular form 24990.2.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.