Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3360c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.c3 3360c1 \([0, -1, 0, -19846, -1069280]\) \(13507798771700416/3544416225\) \(226842638400\) \([2, 2]\) \(7680\) \(1.1637\) \(\Gamma_0(N)\)-optimal
3360.c1 3360c2 \([0, -1, 0, -317521, -68760575]\) \(864335783029582144/59535\) \(243855360\) \([2]\) \(15360\) \(1.5103\)  
3360.c2 3360c3 \([0, -1, 0, -22296, -786060]\) \(2394165105226952/854262178245\) \(437382235261440\) \([2]\) \(15360\) \(1.5103\)  
3360.c4 3360c4 \([0, -1, 0, -17416, -1343384]\) \(-1141100604753992/875529151875\) \(-448270925760000\) \([2]\) \(15360\) \(1.5103\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3360.2.a.c

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.