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SageMath
E = EllipticCurve("gc1")
E.isogeny_class()
Elliptic curves in class 324800gc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 324800.gc2 | 324800gc1 | \([0, -1, 0, -212833, 44829537]\) | \(-1041220466500/242597383\) | \(-248419720192000000\) | \([2]\) | \(3538944\) | \(2.0572\) | \(\Gamma_0(N)\)-optimal |
| 324800.gc1 | 324800gc2 | \([0, -1, 0, -3576833, 2604833537]\) | \(2471097448795250/98942809\) | \(202634872832000000\) | \([2]\) | \(7077888\) | \(2.4038\) |
Rank
sage: E.rank()
The elliptic curves in class 324800gc have rank \(0\).
Complex multiplication
The elliptic curves in class 324800gc do not have complex multiplication.Modular form 324800.2.a.gc
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 Cremona 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 Cremona labels.
