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Properties

Label 18785.b
Number of curves $2$
Conductor $18785$
CM no
Rank $0$
Graph

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

Elliptic curves in class 18785.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18785.b1 18785c1 \([1, 1, 1, -295, 292]\) \(117649/65\) \(1568941985\) \([2]\) \(10240\) \(0.45499\) \(\Gamma_0(N)\)-optimal
18785.b2 18785c2 \([1, 1, 1, 1150, 3760]\) \(6967871/4225\) \(-101981229025\) \([2]\) \(20480\) \(0.80157\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18785.b have rank \(0\).

Complex multiplication

The elliptic curves in class 18785.b do not have complex multiplication.

Modular form 18785.2.a.b

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.