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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 2880.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2880.ba1 | 2880p4 | \([0, 0, 0, -5772, 168784]\) | \(890277128/15\) | \(358318080\) | \([4]\) | \(2048\) | \(0.77168\) | |
| 2880.ba2 | 2880p3 | \([0, 0, 0, -1452, -18704]\) | \(14172488/1875\) | \(44789760000\) | \([2]\) | \(2048\) | \(0.77168\) | |
| 2880.ba3 | 2880p2 | \([0, 0, 0, -372, 2464]\) | \(1906624/225\) | \(671846400\) | \([2, 2]\) | \(1024\) | \(0.42511\) | |
| 2880.ba4 | 2880p1 | \([0, 0, 0, 33, 196]\) | \(85184/405\) | \(-18895680\) | \([2]\) | \(512\) | \(0.078535\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2880.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 2880.ba do not have complex multiplication.Modular form 2880.2.a.ba
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
