Properties

Label 784.e
Number of curves $4$
Conductor $784$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 784.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
784.e1 784c4 \([0, 0, 0, -14651, 682570]\) \(1443468546/7\) \(1686616064\) \([4]\) \(768\) \(0.97092\)  
784.e2 784c3 \([0, 0, 0, -2891, -47334]\) \(11090466/2401\) \(578509309952\) \([2]\) \(768\) \(0.97092\)  
784.e3 784c2 \([0, 0, 0, -931, 10290]\) \(740772/49\) \(5903156224\) \([2, 2]\) \(384\) \(0.62435\)  
784.e4 784c1 \([0, 0, 0, 49, 686]\) \(432/7\) \(-210827008\) \([2]\) \(192\) \(0.27778\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 784.e have rank \(0\).

Complex multiplication

The elliptic curves in class 784.e do not have complex multiplication.

Modular form 784.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.