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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 39600.cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39600.cj1 | 39600cy4 | \([0, 0, 0, -213075, 37847250]\) | \(22930509321/6875\) | \(320760000000000\) | \([2]\) | \(196608\) | \(1.7615\) | |
39600.cj2 | 39600cy3 | \([0, 0, 0, -105075, -12804750]\) | \(2749884201/73205\) | \(3415452480000000\) | \([2]\) | \(196608\) | \(1.7615\) | |
39600.cj3 | 39600cy2 | \([0, 0, 0, -15075, 425250]\) | \(8120601/3025\) | \(141134400000000\) | \([2, 2]\) | \(98304\) | \(1.4149\) | |
39600.cj4 | 39600cy1 | \([0, 0, 0, 2925, 47250]\) | \(59319/55\) | \(-2566080000000\) | \([2]\) | \(49152\) | \(1.0684\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 39600.cj have rank \(1\).
Complex multiplication
The elliptic curves in class 39600.cj do not have complex multiplication.Modular form 39600.2.a.cj
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.