Show commands:
SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 62400.en
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.en1 | 62400dk2 | \([0, 1, 0, -10273, -71617]\) | \(3659383421/2056392\) | \(67383853056000\) | \([2]\) | \(147456\) | \(1.3436\) | |
62400.en2 | 62400dk1 | \([0, 1, 0, 2527, -7617]\) | \(54439939/32448\) | \(-1063256064000\) | \([2]\) | \(73728\) | \(0.99701\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62400.en have rank \(1\).
Complex multiplication
The elliptic curves in class 62400.en do not have complex multiplication.Modular form 62400.2.a.en
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.