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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 129430.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129430.g1 | 129430k4 | \([1, -1, 0, -494954, 134145210]\) | \(2121328796049/120050\) | \(758879634032450\) | \([2]\) | \(1290240\) | \(1.9196\) | |
129430.g2 | 129430k3 | \([1, -1, 0, -162134, -23441362]\) | \(74565301329/5468750\) | \(34569954174218750\) | \([2]\) | \(1290240\) | \(1.9196\) | |
129430.g3 | 129430k2 | \([1, -1, 0, -32704, 1849260]\) | \(611960049/122500\) | \(774366973502500\) | \([2, 2]\) | \(645120\) | \(1.5730\) | |
129430.g4 | 129430k1 | \([1, -1, 0, 4276, 170368]\) | \(1367631/2800\) | \(-17699816537200\) | \([2]\) | \(322560\) | \(1.2264\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129430.g have rank \(0\).
Complex multiplication
The elliptic curves in class 129430.g do not have complex multiplication.Modular form 129430.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.