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Properties

Label 37830.bd
Number of curves $2$
Conductor $37830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 37830.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37830.bd1 37830z2 \([1, 0, 0, -30210785, -78726061395]\) \(-3049367333151487003072932241/912595054886227747515780\) \(-912595054886227747515780\) \([]\) \(7990528\) \(3.3117\)  
37830.bd2 37830z1 \([1, 0, 0, -619685, 230436225]\) \(-26317019808774730149841/7720094603520000000\) \(-7720094603520000000\) \([7]\) \(1141504\) \(2.3388\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37830.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 37830.bd do not have complex multiplication.

Modular form 37830.2.a.bd

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.