Properties

Label 101640.v
Number of curves $6$
Conductor $101640$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 101640.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101640.v1 101640k6 \([0, -1, 0, -2952440, 1953137100]\) \(784478485879202/221484375\) \(803580069600000000\) \([2]\) \(2621440\) \(2.4167\)  
101640.v2 101640k4 \([0, -1, 0, -208160, 22261692]\) \(549871953124/200930625\) \(364503919570560000\) \([2, 2]\) \(1310720\) \(2.0701\)  
101640.v3 101640k2 \([0, -1, 0, -89580, -10039500]\) \(175293437776/4862025\) \(2205023710982400\) \([2, 2]\) \(655360\) \(1.7235\)  
101640.v4 101640k1 \([0, -1, 0, -88975, -10185668]\) \(2748251600896/2205\) \(62500672080\) \([2]\) \(327680\) \(1.3770\) \(\Gamma_0(N)\)-optimal
101640.v5 101640k3 \([0, -1, 0, 19320, -32995620]\) \(439608956/259416045\) \(-470601060450554880\) \([2]\) \(1310720\) \(2.0701\)  
101640.v6 101640k5 \([0, -1, 0, 638840, 156765292]\) \(7947184069438/7533176175\) \(-27331545329170790400\) \([2]\) \(2621440\) \(2.4167\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101640.v have rank \(1\).

Complex multiplication

The elliptic curves in class 101640.v do not have complex multiplication.

Modular form 101640.2.a.v

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.