Properties

Label 840i
Number of curves $4$
Conductor $840$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 840i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
840.i3 840i1 \([0, 1, 0, -36, -96]\) \(20720464/105\) \(26880\) \([2]\) \(64\) \(-0.30352\) \(\Gamma_0(N)\)-optimal
840.i2 840i2 \([0, 1, 0, -56, 0]\) \(19307236/11025\) \(11289600\) \([2, 2]\) \(128\) \(0.043052\)  
840.i1 840i3 \([0, 1, 0, -656, 6240]\) \(15267472418/36015\) \(73758720\) \([2]\) \(256\) \(0.38963\)  
840.i4 840i4 \([0, 1, 0, 224, 224]\) \(604223422/354375\) \(-725760000\) \([2]\) \(256\) \(0.38963\)  

Rank

sage: E.rank()
 

The elliptic curves in class 840i have rank \(0\).

Complex multiplication

The elliptic curves in class 840i do not have complex multiplication.

Modular form 840.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} + 2 q^{13} - q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.