Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 50820e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50820.e2 | 50820e1 | \([0, -1, 0, -2581, -157430]\) | \(-67108864/343035\) | \(-9723318842160\) | \([2]\) | \(115200\) | \(1.1764\) | \(\Gamma_0(N)\)-optimal |
50820.e1 | 50820e2 | \([0, -1, 0, -62476, -5979224]\) | \(59466754384/121275\) | \(55000591430400\) | \([2]\) | \(230400\) | \(1.5230\) |
Rank
sage: E.rank()
The elliptic curves in class 50820e have rank \(0\).
Complex multiplication
The elliptic curves in class 50820e do not have complex multiplication.Modular form 50820.2.a.e
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 Cremona 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 Cremona labels.