Properties

Label 37485.p
Number of curves $2$
Conductor $37485$
CM no
Rank $0$
Graph

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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)
 
\(q - q^{2} - q^{4} - q^{5} + 3 q^{8} + q^{10} + 4 q^{11} + 4 q^{13} - q^{16} + q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.