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Properties

Label 37030f
Number of curves $2$
Conductor $37030$
CM no
Rank $1$
Graph

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

Elliptic curves in class 37030f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37030.f2 37030f1 \([1, -1, 0, -5090, 126100]\) \(1198785674367/140492800\) \(1709375897600\) \([2]\) \(64512\) \(1.0788\) \(\Gamma_0(N)\)-optimal
37030.f1 37030f2 \([1, -1, 0, -19810, -936684]\) \(70665260180607/9411920000\) \(114514830640000\) \([2]\) \(129024\) \(1.4254\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37030f have rank \(1\).

Complex multiplication

The elliptic curves in class 37030f do not have complex multiplication.

Modular form 37030.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} - 3 q^{9} + q^{10} + 2 q^{11} - 4 q^{13} - q^{14} + q^{16} + 6 q^{17} + 3 q^{18} - 4 q^{19} + O(q^{20})\) 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 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.