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SageMath
E = EllipticCurve("nk1")
E.isogeny_class()
Elliptic curves in class 327600nk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327600.nk4 | 327600nk1 | \([0, 0, 0, 2188950, 1354856375]\) | \(6364491337435136/8034291412875\) | \(-1464249609996468750000\) | \([2]\) | \(17694720\) | \(2.7473\) | \(\Gamma_0(N)\)-optimal |
| 327600.nk3 | 327600nk2 | \([0, 0, 0, -13211175, 13105151750]\) | \(87450143958975184/25164018140625\) | \(73378276898062500000000\) | \([2, 2]\) | \(35389440\) | \(3.0939\) | |
| 327600.nk1 | 327600nk3 | \([0, 0, 0, -193800675, 1038311743250]\) | \(69014771940559650916/9797607421875\) | \(114279292968750000000000\) | \([2]\) | \(70778880\) | \(3.4405\) | |
| 327600.nk2 | 327600nk4 | \([0, 0, 0, -79023675, -260082535750]\) | \(4678944235881273796/202428825314625\) | \(2361129818469786000000000\) | \([2]\) | \(70778880\) | \(3.4405\) |
Rank
sage: E.rank()
The elliptic curves in class 327600nk have rank \(0\).
Complex multiplication
The elliptic curves in class 327600nk do not have complex multiplication.Modular form 327600.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
