Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 200158.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200158.n1 | 200158b2 | \([1, 0, 0, -108086, -2606972]\) | \(234770924809/130960928\) | \(77898614114201888\) | \([2]\) | \(3870720\) | \(1.9315\) | |
200158.n2 | 200158b1 | \([1, 0, 0, 26474, -319452]\) | \(3449795831/2071552\) | \(-1232207440264192\) | \([2]\) | \(1935360\) | \(1.5849\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 200158.n have rank \(0\).
Complex multiplication
The elliptic curves in class 200158.n do not have complex multiplication.Modular form 200158.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.