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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 2880bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2880.b4 | 2880bc1 | \([0, 0, 0, 132, -272]\) | \(21296/15\) | \(-179159040\) | \([2]\) | \(1024\) | \(0.27214\) | \(\Gamma_0(N)\)-optimal |
2880.b3 | 2880bc2 | \([0, 0, 0, -588, -2288]\) | \(470596/225\) | \(10749542400\) | \([2, 2]\) | \(2048\) | \(0.61871\) | |
2880.b1 | 2880bc3 | \([0, 0, 0, -7788, -264368]\) | \(546718898/405\) | \(38698352640\) | \([2]\) | \(4096\) | \(0.96528\) | |
2880.b2 | 2880bc4 | \([0, 0, 0, -4908, 130768]\) | \(136835858/1875\) | \(179159040000\) | \([2]\) | \(4096\) | \(0.96528\) |
Rank
sage: E.rank()
The elliptic curves in class 2880bc have rank \(1\).
Complex multiplication
The elliptic curves in class 2880bc do not have complex multiplication.Modular form 2880.2.a.bc
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.