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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 25230.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25230.i1 | 25230g2 | \([1, 0, 1, -110189, -14062864]\) | \(248739515569/504600\) | \(300147847776600\) | \([2]\) | \(161280\) | \(1.6647\) | |
25230.i2 | 25230g1 | \([1, 0, 1, -9269, -55168]\) | \(148035889/83520\) | \(49679643769920\) | \([2]\) | \(80640\) | \(1.3181\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25230.i have rank \(0\).
Complex multiplication
The elliptic curves in class 25230.i do not have complex multiplication.Modular form 25230.2.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 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.