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Properties

Label 37030.m
Number of curves $2$
Conductor $37030$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 37030.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37030.m1 37030k2 \([1, 0, 1, -279588, -67188702]\) \(-30864153721/7024640\) \(-550106479644323840\) \([]\) \(635904\) \(2.1240\)  
37030.m2 37030k1 \([1, 0, 1, 24587, 581488]\) \(20991479/14000\) \(-1096353793934000\) \([3]\) \(211968\) \(1.5746\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37030.m have rank \(0\).

Complex multiplication

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

Modular form 37030.2.a.m

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 LMFDB 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 LMFDB labels.