↑

Properties

Label 37570.h
Number of curves $2$
Conductor $37570$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 37570.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37570.h1 37570q1 \([1, 0, 0, -243055, -46135623]\) \(65787589563409/10400000\) \(251030717600000\) \([2]\) \(409600\) \(1.7736\) \(\Gamma_0(N)\)-optimal
37570.h2 37570q2 \([1, 0, 0, -219935, -55258775]\) \(-48743122863889/26406250000\) \(-637382681406250000\) \([2]\) \(819200\) \(2.1201\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37570.h have rank \(1\).

Complex multiplication

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

Modular form 37570.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} + q^{5} - 2 q^{6} + 4 q^{7} + q^{8} + q^{9} + q^{10} + 2 q^{11} - 2 q^{12} - q^{13} + 4 q^{14} - 2 q^{15} + q^{16} + q^{18} + 6 q^{19} + O(q^{20})\) 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.