Properties

Label 3600.u
Number of curves $8$
Conductor $3600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3600.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.u1 3600bf7 \([0, 0, 0, -7776075, -8346199750]\) \(1114544804970241/405\) \(18895680000000\) \([2]\) \(49152\) \(2.3380\)  
3600.u2 3600bf5 \([0, 0, 0, -486075, -130369750]\) \(272223782641/164025\) \(7652750400000000\) \([2, 2]\) \(24576\) \(1.9915\)  
3600.u3 3600bf8 \([0, 0, 0, -396075, -180139750]\) \(-147281603041/215233605\) \(-10041939074880000000\) \([2]\) \(49152\) \(2.3380\)  
3600.u4 3600bf4 \([0, 0, 0, -288075, 59512250]\) \(56667352321/15\) \(699840000000\) \([4]\) \(12288\) \(1.6449\)  
3600.u5 3600bf3 \([0, 0, 0, -36075, -1219750]\) \(111284641/50625\) \(2361960000000000\) \([2, 2]\) \(12288\) \(1.6449\)  
3600.u6 3600bf2 \([0, 0, 0, -18075, 922250]\) \(13997521/225\) \(10497600000000\) \([2, 2]\) \(6144\) \(1.2983\)  
3600.u7 3600bf1 \([0, 0, 0, -75, 40250]\) \(-1/15\) \(-699840000000\) \([2]\) \(3072\) \(0.95175\) \(\Gamma_0(N)\)-optimal
3600.u8 3600bf6 \([0, 0, 0, 125925, -9157750]\) \(4733169839/3515625\) \(-164025000000000000\) \([2]\) \(24576\) \(1.9915\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3600.u have rank \(1\).

Complex multiplication

The elliptic curves in class 3600.u do not have complex multiplication.

Modular form 3600.2.a.u

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

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.