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SageMath
E = EllipticCurve("ig1")
E.isogeny_class()
Elliptic curves in class 124950.ig
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
124950.ig1 | 124950hh2 | \([1, 0, 0, -66088, -3981958]\) | \(5956317014383/2172381210\) | \(11642605547343750\) | \([2]\) | \(884736\) | \(1.7832\) | |
124950.ig2 | 124950hh1 | \([1, 0, 0, 12662, -438208]\) | \(41890384817/39795300\) | \(-213277935937500\) | \([2]\) | \(442368\) | \(1.4366\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 124950.ig have rank \(0\).
Complex multiplication
The elliptic curves in class 124950.ig do not have complex multiplication.Modular form 124950.2.a.ig
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.