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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 18200.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18200.r1 | 18200e1 | \([0, 0, 0, -338075, 75659750]\) | \(267080942160036/1990625\) | \(31850000000000\) | \([2]\) | \(107520\) | \(1.7670\) | \(\Gamma_0(N)\)-optimal |
| 18200.r2 | 18200e2 | \([0, 0, 0, -331075, 78942750]\) | \(-125415986034978/11552734375\) | \(-369687500000000000\) | \([2]\) | \(215040\) | \(2.1135\) |
Rank
sage: E.rank()
The elliptic curves in class 18200.r have rank \(0\).
Complex multiplication
The elliptic curves in class 18200.r do not have complex multiplication.Modular form 18200.2.a.r
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.
