Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 2850.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2850.z1 | 2850w2 | \([1, 0, 0, -496888, -134878108]\) | \(-1389310279182025/267418692\) | \(-2611510664062500\) | \([]\) | \(36000\) | \(1.9587\) | |
2850.z2 | 2850w1 | \([1, 0, 0, 4772, 7952]\) | \(480705753733655/279172334592\) | \(-6979308364800\) | \([5]\) | \(7200\) | \(1.1539\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2850.z have rank \(1\).
Complex multiplication
The elliptic curves in class 2850.z do not have complex multiplication.Modular form 2850.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.