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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 35490cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35490.cq4 | 35490cn1 | \([1, 1, 1, 1095, 462327]\) | \(30080231/19110000\) | \(-92240319990000\) | \([4]\) | \(129024\) | \(1.3587\) | \(\Gamma_0(N)\)-optimal |
| 35490.cq3 | 35490cn2 | \([1, 1, 1, -83405, 9013727]\) | \(13293525831769/365192100\) | \(1762712515008900\) | \([2, 2]\) | \(258048\) | \(1.7052\) | |
| 35490.cq2 | 35490cn3 | \([1, 1, 1, -193255, -19854853]\) | \(165369706597369/60703354530\) | \(293003497975594770\) | \([2]\) | \(516096\) | \(2.0518\) | |
| 35490.cq1 | 35490cn4 | \([1, 1, 1, -1325555, 586861907]\) | \(53365044437418169/41984670\) | \(202651983018030\) | \([2]\) | \(516096\) | \(2.0518\) |
Rank
sage: E.rank()
The elliptic curves in class 35490cn have rank \(1\).
Complex multiplication
The elliptic curves in class 35490cn do not have complex multiplication.Modular form 35490.2.a.cn
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.
