Properties

Label 348726by
Number of curves $2$
Conductor $348726$
CM no
Rank $1$
Graph

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

Elliptic curves in class 348726by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348726.by1 348726by1 \([1, 1, 1, -1518, 20523]\) \(56402207875/4451328\) \(30531658752\) \([2]\) \(307200\) \(0.75560\) \(\Gamma_0(N)\)-optimal
348726.by2 348726by2 \([1, 1, 1, 1522, 95915]\) \(56844576125/604685088\) \(-4147535018592\) \([2]\) \(614400\) \(1.1022\)  

Rank

sage: E.rank()
 

The elliptic curves in class 348726by have rank \(1\).

Complex multiplication

The elliptic curves in class 348726by do not have complex multiplication.

Modular form 348726.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} + q^{9} - q^{12} + 2q^{13} + q^{14} + q^{16} - 6q^{17} + q^{18} + O(q^{20})\)  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 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.