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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 20800.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20800.j1 | 20800cr1 | \([0, 1, 0, -1345633, 600280863]\) | \(65787589563409/10400000\) | \(42598400000000000\) | \([2]\) | \(368640\) | \(2.2014\) | \(\Gamma_0(N)\)-optimal |
| 20800.j2 | 20800cr2 | \([0, 1, 0, -1217633, 719192863]\) | \(-48743122863889/26406250000\) | \(-108160000000000000000\) | \([2]\) | \(737280\) | \(2.5480\) |
Rank
sage: E.rank()
The elliptic curves in class 20800.j have rank \(0\).
Complex multiplication
The elliptic curves in class 20800.j do not have complex multiplication.Modular form 20800.2.a.j
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.
