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Properties

Label 60990.bh
Number of curves $3$
Conductor $60990$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 60990.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60990.bh1 60990bj3 \([1, 0, 0, -165638790, -821071057998]\) \(-502585390635922447924416132961/378299752139695192905390\) \(-378299752139695192905390\) \([]\) \(13226976\) \(3.4571\)  
60990.bh2 60990bj1 \([1, 0, 0, -231240, 187785792]\) \(-1367453954870275397761/14445609579000000000\) \(-14445609579000000000\) \([9]\) \(1469664\) \(2.3585\) \(\Gamma_0(N)\)-optimal
60990.bh3 60990bj2 \([1, 0, 0, 2063760, -4837643208]\) \(972078350597918586282239/10673270244457546419000\) \(-10673270244457546419000\) \([3]\) \(4408992\) \(2.9078\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60990.bh have rank \(1\).

Complex multiplication

The elliptic curves in class 60990.bh do not have complex multiplication.

Modular form 60990.2.a.bh

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

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.