Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 75810.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75810.n1 | 75810j2 | \([1, 1, 0, -16138, -795788]\) | \(67772591234011/5715360\) | \(39201654240\) | \([2]\) | \(172800\) | \(1.0759\) | |
75810.n2 | 75810j1 | \([1, 1, 0, -938, -14508]\) | \(-13328910811/4838400\) | \(-33186585600\) | \([2]\) | \(86400\) | \(0.72930\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 75810.n have rank \(0\).
Complex multiplication
The elliptic curves in class 75810.n do not have complex multiplication.Modular form 75810.2.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.