Properties

Label 3360.q
Number of curves $4$
Conductor $3360$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3360.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.q1 3360u2 \([0, 1, 0, -324016, -71098216]\) \(7347751505995469192/72930375\) \(37340352000\) \([2]\) \(15360\) \(1.6049\)  
3360.q2 3360u3 \([0, 1, 0, -29016, -67716]\) \(5276930158229192/3050936350875\) \(1562079411648000\) \([2]\) \(15360\) \(1.6049\)  
3360.q3 3360u1 \([0, 1, 0, -20266, -1114216]\) \(14383655824793536/45209390625\) \(2893401000000\) \([2, 2]\) \(7680\) \(1.2583\) \(\Gamma_0(N)\)-optimal
3360.q4 3360u4 \([0, 1, 0, -11761, -2048065]\) \(-43927191786304/415283203125\) \(-1701000000000000\) \([2]\) \(15360\) \(1.6049\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3360.q have rank \(0\).

Complex multiplication

The elliptic curves in class 3360.q do not have complex multiplication.

Modular form 3360.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} - 4q^{11} - 2q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.