Properties

Label 53816.d
Number of curves $4$
Conductor $53816$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53816.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53816.d1 53816c4 \([0, 0, 0, -287339, -59284090]\) \(1443468546/7\) \(12723252770816\) \([2]\) \(230400\) \(1.7150\)  
53816.d2 53816c3 \([0, 0, 0, -56699, 4111158]\) \(11090466/2401\) \(4364075700389888\) \([2]\) \(230400\) \(1.7150\)  
53816.d3 53816c2 \([0, 0, 0, -18259, -893730]\) \(740772/49\) \(44531384697856\) \([2, 2]\) \(115200\) \(1.3684\)  
53816.d4 53816c1 \([0, 0, 0, 961, -59582]\) \(432/7\) \(-1590406596352\) \([2]\) \(57600\) \(1.0218\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 53816.d have rank \(1\).

Complex multiplication

The elliptic curves in class 53816.d do not have complex multiplication.

Modular form 53816.2.a.d

sage: E.q_eigenform(10)
 
\(q + 2q^{5} - q^{7} - 3q^{9} + 4q^{11} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.