Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 24990.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24990.n1 | 24990l2 | \([1, 1, 0, -1292, 15576]\) | \(696213191647/75845160\) | \(26014889880\) | \([2]\) | \(24576\) | \(0.73222\) | |
24990.n2 | 24990l1 | \([1, 1, 0, 108, 1296]\) | \(400315553/2203200\) | \(-755697600\) | \([2]\) | \(12288\) | \(0.38565\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24990.n have rank \(1\).
Complex multiplication
The elliptic curves in class 24990.n do not have complex multiplication.Modular form 24990.2.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.