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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 92400.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.i1 | 92400ex2 | \([0, -1, 0, -112208, 1902912]\) | \(19530306557/11114334\) | \(88914672000000000\) | \([2]\) | \(737280\) | \(1.9421\) | |
92400.i2 | 92400ex1 | \([0, -1, 0, 27792, 222912]\) | \(296740963/174636\) | \(-1397088000000000\) | \([2]\) | \(368640\) | \(1.5955\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.i have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.i do not have complex multiplication.Modular form 92400.2.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.