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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 14400.ej
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14400.ej1 | 14400er2 | \([0, 0, 0, -1740, -26800]\) | \(195112/9\) | \(26873856000\) | \([2]\) | \(12288\) | \(0.76270\) | |
14400.ej2 | 14400er1 | \([0, 0, 0, 60, -1600]\) | \(64/3\) | \(-1119744000\) | \([2]\) | \(6144\) | \(0.41612\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14400.ej have rank \(0\).
Complex multiplication
The elliptic curves in class 14400.ej do not have complex multiplication.Modular form 14400.2.a.ej
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.