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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 50400ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50400.i2 | 50400ci1 | \([0, 0, 0, -112425, 1079500]\) | \(5820343774272/3349609375\) | \(90439453125000000\) | \([2]\) | \(368640\) | \(1.9432\) | \(\Gamma_0(N)\)-optimal |
50400.i1 | 50400ci2 | \([0, 0, 0, -1284300, 558892000]\) | \(135574940230848/367653125\) | \(635304600000000000\) | \([2]\) | \(737280\) | \(2.2898\) |
Rank
sage: E.rank()
The elliptic curves in class 50400ci have rank \(0\).
Complex multiplication
The elliptic curves in class 50400ci do not have complex multiplication.Modular form 50400.2.a.ci
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.