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Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 37030b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37030.l2 37030b1 \([1, 0, 1, 46, -44]\) \(20991479/14000\) \(-7406000\) \([]\) \(9216\) \(0.0069015\) \(\Gamma_0(N)\)-optimal
37030.l1 37030b2 \([1, 0, 1, -529, 5476]\) \(-30864153721/7024640\) \(-3716034560\) \([]\) \(27648\) \(0.55621\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37030b have rank \(2\).

Complex multiplication

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

Modular form 37030.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} - 2 q^{9} + q^{10} - 3 q^{11} + q^{12} + 2 q^{13} + q^{14} - q^{15} + q^{16} + 3 q^{17} + 2 q^{18} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.