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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 17325.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17325.n1 | 17325s5 | \([1, -1, 1, -686070005, 6916900543872]\) | \(3135316978843283198764801/571725\) | \(6512305078125\) | \([2]\) | \(1474560\) | \(3.2532\) | |
| 17325.n2 | 17325s4 | \([1, -1, 1, -42879380, 108084587622]\) | \(765458482133960722801/326869475625\) | \(3723247620791015625\) | \([2, 2]\) | \(737280\) | \(2.9066\) | |
| 17325.n3 | 17325s6 | \([1, -1, 1, -42666755, 109209373872]\) | \(-754127868744065783521/15825714261328125\) | \(-180264776507940673828125\) | \([2]\) | \(1474560\) | \(3.2532\) | |
| 17325.n4 | 17325s3 | \([1, -1, 1, -5725130, -2779063878]\) | \(1821931919215868881/761147600816295\) | \(8669946890548110234375\) | \([2]\) | \(737280\) | \(2.9066\) | |
| 17325.n5 | 17325s2 | \([1, -1, 1, -2693255, 1671728622]\) | \(189674274234120481/3859869269025\) | \(43966323392487890625\) | \([2, 2]\) | \(368640\) | \(2.5600\) | |
| 17325.n6 | 17325s1 | \([1, -1, 1, 7870, 78064872]\) | \(4733169839/231139696095\) | \(-2632825600832109375\) | \([2]\) | \(184320\) | \(2.2134\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17325.n have rank \(1\).
Complex multiplication
The elliptic curves in class 17325.n do not have complex multiplication.Modular form 17325.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
