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Properties

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

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 37830bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37830.ba1 37830bc1 \([1, 0, 0, -240, -900]\) \(1529221973761/550426500\) \(550426500\) \([2]\) \(20736\) \(0.37790\) \(\Gamma_0(N)\)-optimal
37830.ba2 37830bc2 \([1, 0, 0, 730, -6138]\) \(43018484764319/41494781250\) \(-41494781250\) \([2]\) \(41472\) \(0.72448\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 37830.2.a.bc

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