Properties

Label 5776.m
Number of curves $3$
Conductor $5776$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5776.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5776.m1 5776l3 \([0, 1, 0, -493968, -1075051756]\) \(-69173457625/2550136832\) \(-491411185385426911232\) \([]\) \(155520\) \(2.6505\)  
5776.m2 5776l1 \([0, 1, 0, -89648, 10304852]\) \(-413493625/152\) \(-29290389143552\) \([]\) \(17280\) \(1.5519\) \(\Gamma_0(N)\)-optimal
5776.m3 5776l2 \([0, 1, 0, 54752, 39288820]\) \(94196375/3511808\) \(-676725150772625408\) \([]\) \(51840\) \(2.1012\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5776.m have rank \(1\).

Complex multiplication

The elliptic curves in class 5776.m do not have complex multiplication.

Modular form 5776.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} - 2q^{9} + 6q^{11} - 5q^{13} + 3q^{17} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.