Properties

Label 369600.rr
Number of curves $6$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("rr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.rr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.rr1 369600rr4 \([0, 1, 0, -142737488033, -20756598437147937]\) \(78519570041710065450485106721/96428056919040\) \(394969321140387840000000\) \([2]\) \(849346560\) \(4.7019\)  
369600.rr2 369600rr5 \([0, 1, 0, -41981776033, 3030354502628063]\) \(1997773216431678333214187041/187585177195046990066400\) \(768348885790912471311974400000000\) \([2]\) \(1698693120\) \(5.0484\)  
369600.rr3 369600rr3 \([0, 1, 0, -9322576033, -293535577371937]\) \(21876183941534093095979041/3572502915711058560000\) \(14632971942752495861760000000000\) \([2, 2]\) \(849346560\) \(4.7019\)  
369600.rr4 369600rr2 \([0, 1, 0, -8921168033, -324318352667937]\) \(19170300594578891358373921/671785075055001600\) \(2751631667425286553600000000\) \([2, 2]\) \(424673280\) \(4.3553\)  
369600.rr5 369600rr1 \([0, 1, 0, -532560033, -5542860059937]\) \(-4078208988807294650401/880065599546327040\) \(-3604748695741755555840000000\) \([2]\) \(212336640\) \(4.0087\) \(\Gamma_0(N)\)-optimal
369600.rr6 369600rr6 \([0, 1, 0, 16914095967, -1647321615899937]\) \(130650216943167617311657439/361816948816603087500000\) \(-1482002222352806246400000000000000\) \([2]\) \(1698693120\) \(5.0484\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600.rr have rank \(0\).

Complex multiplication

The elliptic curves in class 369600.rr do not have complex multiplication.

Modular form 369600.2.a.rr

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - q^{11} - 2 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.