Properties

Label 26640be
Number of curves $6$
Conductor $26640$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 26640be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
26640.p5 26640be1 \([0, 0, 0, -121683, 56241682]\) \(-66730743078481/419010969600\) \(-1251160051050086400\) \([2]\) \(331776\) \(2.1561\) \(\Gamma_0(N)\)-optimal
26640.p4 26640be2 \([0, 0, 0, -3070803, 2066951698]\) \(1072487167529950801/2554882560000\) \(7628838446039040000\) \([2, 2]\) \(663552\) \(2.5027\)  
26640.p3 26640be3 \([0, 0, 0, -4222803, 375124498]\) \(2788936974993502801/1593609593601600\) \(4758492748740879974400\) \([2, 2]\) \(1327104\) \(2.8493\)  
26640.p1 26640be4 \([0, 0, 0, -49104723, 132444219922]\) \(4385367890843575421521/24975000000\) \(74574950400000000\) \([2]\) \(1327104\) \(2.8493\)  
26640.p6 26640be5 \([0, 0, 0, 16772397, 2991126418]\) \(174751791402194852399/102423900876336360\) \(-305836129234326349578240\) \([2]\) \(2654208\) \(3.1958\)  
26640.p2 26640be6 \([0, 0, 0, -43650003, -110517818222]\) \(3080272010107543650001/15465841417699560\) \(46180755019788202967040\) \([2]\) \(2654208\) \(3.1958\)  

Rank

sage: E.rank()
 

The elliptic curves in class 26640be have rank \(0\).

Complex multiplication

The elliptic curves in class 26640be do not have complex multiplication.

Modular form 26640.2.a.be

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.