Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 211420.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
211420.j1 | 211420l2 | \([0, 0, 0, -103447, 12806286]\) | \(16052858101296/75625\) | \(576753760000\) | \([2]\) | \(442368\) | \(1.4588\) | |
211420.j2 | 211420l1 | \([0, 0, 0, -6572, 193161]\) | \(65858420736/4296875\) | \(2048131250000\) | \([2]\) | \(221184\) | \(1.1122\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 211420.j have rank \(2\).
Complex multiplication
The elliptic curves in class 211420.j do not have complex multiplication.Modular form 211420.2.a.j
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.