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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 14994.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14994.u1 | 14994t4 | \([1, -1, 0, -49842, -2947190]\) | \(159661140625/48275138\) | \(4140371326999698\) | \([2]\) | \(82944\) | \(1.7017\) | |
14994.u2 | 14994t3 | \([1, -1, 0, -45432, -3715412]\) | \(120920208625/19652\) | \(1685475809892\) | \([2]\) | \(41472\) | \(1.3552\) | |
14994.u3 | 14994t2 | \([1, -1, 0, -18972, 1010344]\) | \(8805624625/2312\) | \(198291271752\) | \([2]\) | \(27648\) | \(1.1524\) | |
14994.u4 | 14994t1 | \([1, -1, 0, -1332, 11920]\) | \(3048625/1088\) | \(93313539648\) | \([2]\) | \(13824\) | \(0.80587\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14994.u have rank \(1\).
Complex multiplication
The elliptic curves in class 14994.u do not have complex multiplication.Modular form 14994.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.