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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 2240.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2240.r1 | 2240p2 | \([0, 1, 0, -3221, 69299]\) | \(-225637236736/1715\) | \(-28098560\) | \([]\) | \(1152\) | \(0.60412\) | |
| 2240.r2 | 2240p1 | \([0, 1, 0, -21, 179]\) | \(-65536/875\) | \(-14336000\) | \([]\) | \(384\) | \(0.054815\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2240.r have rank \(0\).
Complex multiplication
The elliptic curves in class 2240.r do not have complex multiplication.Modular form 2240.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
