Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 38962e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38962.d2 | 38962e1 | \([1, 0, 1, -1576, -173274]\) | \(-244140625/7169008\) | \(-12700334981488\) | \([2]\) | \(92160\) | \(1.1948\) | \(\Gamma_0(N)\)-optimal |
38962.d1 | 38962e2 | \([1, 0, 1, -57236, -5249466]\) | \(11704814052625/66001628\) | \(116925910101308\) | \([2]\) | \(184320\) | \(1.5414\) |
Rank
sage: E.rank()
The elliptic curves in class 38962e have rank \(2\).
Complex multiplication
The elliptic curves in class 38962e do not have complex multiplication.Modular form 38962.2.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.