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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 2880q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2880.z4 | 2880q1 | \([0, 0, 0, 33, -196]\) | \(85184/405\) | \(-18895680\) | \([2]\) | \(512\) | \(0.078535\) | \(\Gamma_0(N)\)-optimal |
2880.z3 | 2880q2 | \([0, 0, 0, -372, -2464]\) | \(1906624/225\) | \(671846400\) | \([2, 2]\) | \(1024\) | \(0.42511\) | |
2880.z1 | 2880q3 | \([0, 0, 0, -5772, -168784]\) | \(890277128/15\) | \(358318080\) | \([2]\) | \(2048\) | \(0.77168\) | |
2880.z2 | 2880q4 | \([0, 0, 0, -1452, 18704]\) | \(14172488/1875\) | \(44789760000\) | \([4]\) | \(2048\) | \(0.77168\) |
Rank
sage: E.rank()
The elliptic curves in class 2880q have rank \(1\).
Complex multiplication
The elliptic curves in class 2880q do not have complex multiplication.Modular form 2880.2.a.q
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.