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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 230384.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
230384.i1 | 230384i2 | \([0, 1, 0, -54248, 565684]\) | \(2433138625/1387778\) | \(10070152730451968\) | \([2]\) | \(1075200\) | \(1.7605\) | |
230384.i2 | 230384i1 | \([0, 1, 0, -34888, -2508684]\) | \(647214625/3332\) | \(24178037768192\) | \([2]\) | \(537600\) | \(1.4139\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 230384.i have rank \(0\).
Complex multiplication
The elliptic curves in class 230384.i do not have complex multiplication.Modular form 230384.2.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.