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SageMath
E = EllipticCurve("ge1")
E.isogeny_class()
Elliptic curves in class 176400ge
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.pk1 | 176400ge1 | \([0, 0, 0, -58800, -2015125]\) | \(1048576/525\) | \(11256803381250000\) | \([2]\) | \(884736\) | \(1.7728\) | \(\Gamma_0(N)\)-optimal |
| 176400.pk2 | 176400ge2 | \([0, 0, 0, 216825, -15520750]\) | \(3286064/2205\) | \(-756457187220000000\) | \([2]\) | \(1769472\) | \(2.1193\) |
Rank
sage: E.rank()
The elliptic curves in class 176400ge have rank \(0\).
Complex multiplication
The elliptic curves in class 176400ge do not have complex multiplication.Modular form 176400.2.a.ge
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.
