Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 5850e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5850.h2 | 5850e1 | \([1, -1, 0, 3781308, -1679364784]\) | \(19441890357117957/15208161280000\) | \(-4677222476160000000000\) | \([2]\) | \(368640\) | \(2.8461\) | \(\Gamma_0(N)\)-optimal |
| 5850.h1 | 5850e2 | \([1, -1, 0, -17818692, -14488164784]\) | \(2034416504287874043/882294347833600\) | \(271346869506386700000000\) | \([2]\) | \(737280\) | \(3.1926\) |
Rank
sage: E.rank()
The elliptic curves in class 5850e have rank \(0\).
Complex multiplication
The elliptic curves in class 5850e do not have complex multiplication.Modular form 5850.2.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.
