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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 369600.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.v1 | 369600v1 | \([0, -1, 0, -153281633, -293323828863]\) | \(388950302854250851396/188776686710390625\) | \(193307327191440000000000000\) | \([2]\) | \(113541120\) | \(3.7374\) | \(\Gamma_0(N)\)-optimal |
369600.v2 | 369600v2 | \([0, -1, 0, 555306367, -2241232240863]\) | \(9246805402538461809742/6410550311279296875\) | \(-13128807037500000000000000000\) | \([2]\) | \(227082240\) | \(4.0839\) |
Rank
sage: E.rank()
The elliptic curves in class 369600.v have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.v do not have complex multiplication.Modular form 369600.2.a.v
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.