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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2873a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2873.c4 | 2873a1 | \([1, -1, 0, -116, 235]\) | \(35937/17\) | \(82055753\) | \([2]\) | \(576\) | \(0.21269\) | \(\Gamma_0(N)\)-optimal |
| 2873.c2 | 2873a2 | \([1, -1, 0, -961, -11088]\) | \(20346417/289\) | \(1394947801\) | \([2, 2]\) | \(1152\) | \(0.55927\) | |
| 2873.c1 | 2873a3 | \([1, -1, 0, -15326, -726465]\) | \(82483294977/17\) | \(82055753\) | \([2]\) | \(2304\) | \(0.90584\) | |
| 2873.c3 | 2873a4 | \([1, -1, 0, -116, -30523]\) | \(-35937/83521\) | \(-403139914489\) | \([2]\) | \(2304\) | \(0.90584\) |
Rank
sage: E.rank()
The elliptic curves in class 2873a have rank \(0\).
Complex multiplication
The elliptic curves in class 2873a do not have complex multiplication.Modular form 2873.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
