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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2310.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2310.k1 | 2310j4 | \([1, 0, 1, -266113, 52815788]\) | \(2084105208962185000201/31185000\) | \(31185000\) | \([2]\) | \(12288\) | \(1.4415\) | |
2310.k2 | 2310j3 | \([1, 0, 1, -18033, 676876]\) | \(648474704552553481/176469171805080\) | \(176469171805080\) | \([2]\) | \(12288\) | \(1.4415\) | |
2310.k3 | 2310j2 | \([1, 0, 1, -16633, 824156]\) | \(508859562767519881/62240270400\) | \(62240270400\) | \([2, 2]\) | \(6144\) | \(1.0950\) | |
2310.k4 | 2310j1 | \([1, 0, 1, -953, 15068]\) | \(-95575628340361/43812679680\) | \(-43812679680\) | \([2]\) | \(3072\) | \(0.74838\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2310.k have rank \(1\).
Complex multiplication
The elliptic curves in class 2310.k do not have complex multiplication.Modular form 2310.2.a.k
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.