Properties

Label 77616.dq
Number of curves $4$
Conductor $77616$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dq1")
 
E.isogeny_class()
 

Elliptic curves in class 77616.dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77616.dq1 77616ex3 \([0, 0, 0, -568155, 164203018]\) \(57736239625/255552\) \(89774914575532032\) \([2]\) \(829440\) \(2.1053\)  
77616.dq2 77616ex4 \([0, 0, 0, -285915, 327394186]\) \(-7357983625/127552392\) \(-44808904237512425472\) \([2]\) \(1658880\) \(2.4519\)  
77616.dq3 77616ex1 \([0, 0, 0, -38955, -2791334]\) \(18609625/1188\) \(417342061559808\) \([2]\) \(276480\) \(1.5560\) \(\Gamma_0(N)\)-optimal
77616.dq4 77616ex2 \([0, 0, 0, 31605, -11780678]\) \(9938375/176418\) \(-61975296141631488\) \([2]\) \(552960\) \(1.9026\)  

Rank

sage: E.rank()
 

The elliptic curves in class 77616.dq have rank \(0\).

Complex multiplication

The elliptic curves in class 77616.dq do not have complex multiplication.

Modular form 77616.2.a.dq

sage: E.q_eigenform(10)
 
\(q - q^{11} + 4 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.