Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 840.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
840.c1 840b3 \([0, -1, 0, -3736, -86660]\) \(5633270409316/14175\) \(14515200\) \([2]\) \(512\) \(0.61247\)  
840.c2 840b4 \([0, -1, 0, -656, 4956]\) \(30534944836/8203125\) \(8400000000\) \([2]\) \(512\) \(0.61247\)  
840.c3 840b2 \([0, -1, 0, -236, -1260]\) \(5702413264/275625\) \(70560000\) \([2, 2]\) \(256\) \(0.26590\)  
840.c4 840b1 \([0, -1, 0, 9, -84]\) \(4499456/180075\) \(-2881200\) \([4]\) \(128\) \(-0.080674\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 840.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} - 2q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.