Properties

Label 37570f
Number of curves $2$
Conductor $37570$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 37570f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37570.k1 37570f1 \([1, -1, 1, -53953, -4090863]\) \(719564007681/114920000\) \(2773889429480000\) \([2]\) \(221184\) \(1.6857\) \(\Gamma_0(N)\)-optimal
37570.k2 37570f2 \([1, -1, 1, 96327, -22905919]\) \(4095232047999/11740625000\) \(-283390146040625000\) \([2]\) \(442368\) \(2.0323\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37570f have rank \(0\).

Complex multiplication

The elliptic curves in class 37570f do not have complex multiplication.

Modular form 37570.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - 3 q^{9} - q^{10} + 6 q^{11} - q^{13} + q^{16} - 3 q^{18} + O(q^{20})\) 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 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.