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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2310.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2310.c1 | 2310c3 | \([1, 1, 0, -12183, 510237]\) | \(200005594092187129/1027287538200\) | \(1027287538200\) | \([2]\) | \(6144\) | \(1.1508\) | |
2310.c2 | 2310c2 | \([1, 1, 0, -1183, -2363]\) | \(183337554283129/104587560000\) | \(104587560000\) | \([2, 2]\) | \(3072\) | \(0.80423\) | |
2310.c3 | 2310c1 | \([1, 1, 0, -863, -10107]\) | \(71210194441849/165580800\) | \(165580800\) | \([2]\) | \(1536\) | \(0.45766\) | \(\Gamma_0(N)\)-optimal |
2310.c4 | 2310c4 | \([1, 1, 0, 4697, -12947]\) | \(11456208593737991/6725709375000\) | \(-6725709375000\) | \([2]\) | \(6144\) | \(1.1508\) |
Rank
sage: E.rank()
The elliptic curves in class 2310.c have rank \(1\).
Complex multiplication
The elliptic curves in class 2310.c do not have complex multiplication.Modular form 2310.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.