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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 369600.ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.ck1 | 369600ck3 | \([0, -1, 0, -78848033, 269511167937]\) | \(13235378341603461121/9240\) | \(37847040000000\) | \([2]\) | \(14155776\) | \(2.8184\) | |
| 369600.ck2 | 369600ck2 | \([0, -1, 0, -4928033, 4212287937]\) | \(3231355012744321/85377600\) | \(349706649600000000\) | \([2, 2]\) | \(7077888\) | \(2.4718\) | |
| 369600.ck3 | 369600ck4 | \([0, -1, 0, -4736033, 4555391937]\) | \(-2868190647517441/527295615000\) | \(-2159802839040000000000\) | \([2]\) | \(14155776\) | \(2.8184\) | |
| 369600.ck4 | 369600ck1 | \([0, -1, 0, -320033, 60479937]\) | \(885012508801/127733760\) | \(523197480960000000\) | \([2]\) | \(3538944\) | \(2.1253\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.ck have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.ck do not have complex multiplication.Modular form 369600.2.a.ck
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.
