Properties

Label 52416.ca
Number of curves $2$
Conductor $52416$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 52416.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52416.ca1 52416fg2 \([0, 0, 0, -2116509708, -37478181565424]\) \(-5486773802537974663600129/2635437714\) \(-503639990208036864\) \([]\) \(12644352\) \(3.6356\)  
52416.ca2 52416fg1 \([0, 0, 0, 411252, -1146942704]\) \(40251338884511/2997011332224\) \(-572737784693731098624\) \([]\) \(1806336\) \(2.6626\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 52416.ca have rank \(0\).

Complex multiplication

The elliptic curves in class 52416.ca do not have complex multiplication.

Modular form 52416.2.a.ca

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 5 q^{11} + q^{13} + 3 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.