Properties

Label 7056.by
Number of curves $2$
Conductor $7056$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("by1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.by1 7056bd2 \([0, 0, 0, -657531, 205242282]\) \(-67645179/8\) \(-3718138366623744\) \([]\) \(72576\) \(2.0132\)  
7056.by2 7056bd1 \([0, 0, 0, 1029, 869162]\) \(189/512\) \(-326420926562304\) \([]\) \(24192\) \(1.4639\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7056.by have rank \(0\).

Complex multiplication

The elliptic curves in class 7056.by do not have complex multiplication.

Modular form 7056.2.a.by

sage: E.q_eigenform(10)
 
\(q + 3q^{5} + 3q^{11} + 2q^{13} + 6q^{17} - 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.