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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 1872.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1872.r1 | 1872l2 | \([0, 0, 0, -2703, 54090]\) | \(315978926832/169\) | \(1168128\) | \([2]\) | \(1536\) | \(0.49389\) | |
| 1872.r2 | 1872l1 | \([0, 0, 0, -168, 855]\) | \(-1213857792/28561\) | \(-12338352\) | \([2]\) | \(768\) | \(0.14731\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1872.r have rank \(0\).
Complex multiplication
The elliptic curves in class 1872.r do not have complex multiplication.Modular form 1872.2.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.
