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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 124545.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
124545.g1 | 124545k4 | \([1, 1, 1, -10878201, -13808835102]\) | \(3026030815665395929/1364501953125\) | \(64194196510986328125\) | \([2]\) | \(8294400\) | \(2.7585\) | |
124545.g2 | 124545k3 | \([1, 1, 1, -5979431, 5527456994]\) | \(502552788401502649/10024505152875\) | \(471611676506044057875\) | \([2]\) | \(8294400\) | \(2.7585\) | |
124545.g3 | 124545k2 | \([1, 1, 1, -790056, -141416256]\) | \(1159246431432649/488076890625\) | \(22962007315193765625\) | \([2, 2]\) | \(4147200\) | \(2.4119\) | |
124545.g4 | 124545k1 | \([1, 1, 1, 164789, -16140592]\) | \(10519294081031/8500170375\) | \(-399898003941975375\) | \([2]\) | \(2073600\) | \(2.0653\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 124545.g have rank \(0\).
Complex multiplication
The elliptic curves in class 124545.g do not have complex multiplication.Modular form 124545.2.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.