Properties

Label 103056.bg
Number of curves $2$
Conductor $103056$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 103056.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
103056.bg1 103056bd1 \([0, 1, 0, -7918136, 5056370772]\) \(13403946614821979039929/5057590268826067968\) \(20715889741111574396928\) \([2]\) \(15175680\) \(2.9817\) \(\Gamma_0(N)\)-optimal
103056.bg2 103056bd2 \([0, 1, 0, 24770504, 36110578772]\) \(410363075617640914325831/374944243169850027552\) \(-1535771620023705712852992\) \([2]\) \(30351360\) \(3.3282\)  

Rank

sage: E.rank()
 

The elliptic curves in class 103056.bg have rank \(0\).

Complex multiplication

The elliptic curves in class 103056.bg do not have complex multiplication.

Modular form 103056.2.a.bg

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4 q^{5} + 4 q^{7} + q^{9} + 4 q^{15} - 6 q^{17} - q^{19} + O(q^{20})\)  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.