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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 2880.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2880.r1 | 2880l4 | \([0, 0, 0, -7788, 264368]\) | \(546718898/405\) | \(38698352640\) | \([2]\) | \(4096\) | \(0.96528\) | |
2880.r2 | 2880l3 | \([0, 0, 0, -4908, -130768]\) | \(136835858/1875\) | \(179159040000\) | \([2]\) | \(4096\) | \(0.96528\) | |
2880.r3 | 2880l2 | \([0, 0, 0, -588, 2288]\) | \(470596/225\) | \(10749542400\) | \([2, 2]\) | \(2048\) | \(0.61871\) | |
2880.r4 | 2880l1 | \([0, 0, 0, 132, 272]\) | \(21296/15\) | \(-179159040\) | \([2]\) | \(1024\) | \(0.27214\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2880.r have rank \(0\).
Complex multiplication
The elliptic curves in class 2880.r do not have complex multiplication.Modular form 2880.2.a.r
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.