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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 2880o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2880.c3 | 2880o1 | \([0, 0, 0, -8103, -280748]\) | \(1261112198464/675\) | \(31492800\) | \([2]\) | \(3072\) | \(0.76837\) | \(\Gamma_0(N)\)-optimal |
2880.c2 | 2880o2 | \([0, 0, 0, -8148, -277472]\) | \(20034997696/455625\) | \(1360488960000\) | \([2, 2]\) | \(6144\) | \(1.1149\) | |
2880.c1 | 2880o3 | \([0, 0, 0, -17868, 511792]\) | \(26410345352/10546875\) | \(251942400000000\) | \([2]\) | \(12288\) | \(1.4615\) | |
2880.c4 | 2880o4 | \([0, 0, 0, 852, -857072]\) | \(2863288/13286025\) | \(-317374864588800\) | \([2]\) | \(12288\) | \(1.4615\) |
Rank
sage: E.rank()
The elliptic curves in class 2880o have rank \(0\).
Complex multiplication
The elliptic curves in class 2880o do not have complex multiplication.Modular form 2880.2.a.o
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.