Properties

Label 3360.p
Number of curves $4$
Conductor $3360$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3360.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.p1 3360k3 \([0, 1, 0, -317521, 68760575]\) \(864335783029582144/59535\) \(243855360\) \([2]\) \(15360\) \(1.5103\)  
3360.p2 3360k2 \([0, 1, 0, -22296, 786060]\) \(2394165105226952/854262178245\) \(437382235261440\) \([2]\) \(15360\) \(1.5103\)  
3360.p3 3360k1 \([0, 1, 0, -19846, 1069280]\) \(13507798771700416/3544416225\) \(226842638400\) \([2, 2]\) \(7680\) \(1.1637\) \(\Gamma_0(N)\)-optimal
3360.p4 3360k4 \([0, 1, 0, -17416, 1343384]\) \(-1141100604753992/875529151875\) \(-448270925760000\) \([2]\) \(15360\) \(1.5103\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3360.p have rank \(1\).

Complex multiplication

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

Modular form 3360.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} - 4q^{11} - 6q^{13} - q^{15} + 6q^{17} + O(q^{20})\)  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.