Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37570g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37570.o2 37570g1 \([1, 1, 1, -3325461, 2009311739]\) \(827813553991775477153/123566310400000000\) \(607081282995200000000\) \([2]\) \(1474560\) \(2.7123\) \(\Gamma_0(N)\)-optimal
37570.o1 37570g2 \([1, 1, 1, -51132181, 140706167803]\) \(3009261308803109129809313/85820312500000000\) \(421635195312500000000\) \([2]\) \(2949120\) \(3.0589\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 37570.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2q^{3} + q^{4} - q^{5} + 2q^{6} + q^{8} + q^{9} - q^{10} + 2q^{12} - q^{13} - 2q^{15} + q^{16} + q^{18} + O(q^{20})\)  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.