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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 8976.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8976.g1 | 8976u1 | \([0, -1, 0, -14464, -659456]\) | \(81706955619457/744505344\) | \(3049493889024\) | \([2]\) | \(26880\) | \(1.2177\) | \(\Gamma_0(N)\)-optimal |
| 8976.g2 | 8976u2 | \([0, -1, 0, -4224, -1585152]\) | \(-2035346265217/264305213568\) | \(-1082594154774528\) | \([2]\) | \(53760\) | \(1.5643\) |
Rank
sage: E.rank()
The elliptic curves in class 8976.g have rank \(1\).
Complex multiplication
The elliptic curves in class 8976.g do not have complex multiplication.Modular form 8976.2.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.
