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SageMath
E = EllipticCurve("ge1")
E.isogeny_class()
Elliptic curves in class 215600ge
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 215600.x2 | 215600ge1 | \([0, 1, 0, -2508, -53012]\) | \(-1272112/121\) | \(-166012000000\) | \([2]\) | \(245760\) | \(0.89463\) | \(\Gamma_0(N)\)-optimal |
| 215600.x1 | 215600ge2 | \([0, 1, 0, -41008, -3210012]\) | \(1389715708/11\) | \(60368000000\) | \([2]\) | \(491520\) | \(1.2412\) |
Rank
sage: E.rank()
The elliptic curves in class 215600ge have rank \(0\).
Complex multiplication
The elliptic curves in class 215600ge do not have complex multiplication.Modular form 215600.2.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.
