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SageMath
E = EllipticCurve("nk1")
E.isogeny_class()
Elliptic curves in class 352800nk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 352800.nk3 | 352800nk1 | \([0, 0, 0, -47697825, -103183661000]\) | \(139927692143296/27348890625\) | \(2345608262559515625000000\) | \([2, 2]\) | \(42467328\) | \(3.3930\) | \(\Gamma_0(N)\)-optimal |
| 352800.nk2 | 352800nk2 | \([0, 0, 0, -233744700, 1282493464000]\) | \(257307998572864/19456203375\) | \(106795717943094936000000000\) | \([2]\) | \(84934656\) | \(3.7395\) | |
| 352800.nk4 | 352800nk3 | \([0, 0, 0, 98162925, -610633210250]\) | \(152461584507448/322998046875\) | \(-221618316568359375000000000\) | \([2]\) | \(84934656\) | \(3.7395\) | |
| 352800.nk1 | 352800nk4 | \([0, 0, 0, -722979075, -7481981879750]\) | \(60910917333827912/3255076125\) | \(2233402022407689000000000\) | \([2]\) | \(84934656\) | \(3.7395\) |
Rank
sage: E.rank()
The elliptic curves in class 352800nk have rank \(1\).
Complex multiplication
The elliptic curves in class 352800nk do not have complex multiplication.Modular form 352800.2.a.nk
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
