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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1890.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1890.c1 | 1890g1 | \([1, -1, 0, -219945, 39757665]\) | \(-43581616978927713867/6860\) | \(-185220\) | \([3]\) | \(6480\) | \(1.3270\) | \(\Gamma_0(N)\)-optimal |
1890.c2 | 1890g2 | \([1, -1, 0, -219660, 39865616]\) | \(-59550644977653843/322828856000\) | \(-6354240372648000\) | \([3]\) | \(19440\) | \(1.8763\) | |
1890.c3 | 1890g3 | \([1, -1, 0, 567525, 211833125]\) | \(114115456478544693/175616000000000\) | \(-31109847552000000000\) | \([]\) | \(58320\) | \(2.4256\) |
Rank
sage: E.rank()
The elliptic curves in class 1890.c have rank \(1\).
Complex multiplication
The elliptic curves in class 1890.c do not have complex multiplication.Modular form 1890.2.a.c
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.