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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 1890.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1890.x1 | 1890r2 | \([1, -1, 1, -1979507, -1071477449]\) | \(-43581616978927713867/6860\) | \(-135025380\) | \([]\) | \(19440\) | \(1.8763\) | |
| 1890.x2 | 1890r1 | \([1, -1, 1, -24407, -1468369]\) | \(-59550644977653843/322828856000\) | \(-8716379112000\) | \([3]\) | \(6480\) | \(1.3270\) | \(\Gamma_0(N)\)-optimal |
| 1890.x3 | 1890r3 | \([1, -1, 1, 63058, -7866691]\) | \(114115456478544693/175616000000000\) | \(-42674688000000000\) | \([9]\) | \(19440\) | \(1.8763\) |
Rank
sage: E.rank()
The elliptic curves in class 1890.x have rank \(0\).
Complex multiplication
The elliptic curves in class 1890.x do not have complex multiplication.Modular form 1890.2.a.x
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
