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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 3675.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3675.n1 | 3675j5 | \([1, 0, 1, -960426, 362199373]\) | \(53297461115137/147\) | \(270225046875\) | \([2]\) | \(24576\) | \(1.8519\) | |
| 3675.n2 | 3675j4 | \([1, 0, 1, -60051, 5650873]\) | \(13027640977/21609\) | \(39723081890625\) | \([2, 2]\) | \(12288\) | \(1.5053\) | |
| 3675.n3 | 3675j3 | \([1, 0, 1, -47801, -4002127]\) | \(6570725617/45927\) | \(84426025359375\) | \([2]\) | \(12288\) | \(1.5053\) | |
| 3675.n4 | 3675j6 | \([1, 0, 1, -41676, 9178873]\) | \(-4354703137/17294403\) | \(-31791706539796875\) | \([2]\) | \(24576\) | \(1.8519\) | |
| 3675.n5 | 3675j2 | \([1, 0, 1, -4926, 28123]\) | \(7189057/3969\) | \(7296076265625\) | \([2, 2]\) | \(6144\) | \(1.1587\) | |
| 3675.n6 | 3675j1 | \([1, 0, 1, 1199, 3623]\) | \(103823/63\) | \(-115810734375\) | \([2]\) | \(3072\) | \(0.81216\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3675.n have rank \(1\).
Complex multiplication
The elliptic curves in class 3675.n do not have complex multiplication.Modular form 3675.2.a.n
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
