Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 37485.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37485.p1 | 37485be2 | \([1, -1, 1, -263948, -42513208]\) | \(23711636464489/4590075735\) | \(393672990887173935\) | \([2]\) | \(442368\) | \(2.0932\) | |
37485.p2 | 37485be1 | \([1, -1, 1, 33727, -3934528]\) | \(49471280711/106269975\) | \(-9114363534516975\) | \([2]\) | \(221184\) | \(1.7466\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37485.p have rank \(0\).
Complex multiplication
The elliptic curves in class 37485.p do not have complex multiplication.Modular form 37485.2.a.p
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.