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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 4368.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4368.g1 | 4368e2 | \([0, -1, 0, -2668, 32656]\) | \(8207369602000/3046751253\) | \(779968320768\) | \([2]\) | \(3584\) | \(0.98183\) | |
4368.g2 | 4368e1 | \([0, -1, 0, 517, 3354]\) | \(953312000000/887416803\) | \(-14198668848\) | \([2]\) | \(1792\) | \(0.63526\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4368.g have rank \(0\).
Complex multiplication
The elliptic curves in class 4368.g do not have complex multiplication.Modular form 4368.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.