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Properties

Label 3330k
Number of curves $2$
Conductor $3330$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 3330k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3330.h2 3330k1 \([1, -1, 0, -750564, 334125648]\) \(-64144540676215729729/28962038218752000\) \(-21113325861470208000\) \([]\) \(63360\) \(2.4147\) \(\Gamma_0(N)\)-optimal
3330.h1 3330k2 \([1, -1, 0, -66276324, 207692300880]\) \(-44164307457093068844199489/1823508000000000\) \(-1329337332000000000\) \([3]\) \(190080\) \(2.9640\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3330k have rank \(0\).

Complex multiplication

The elliptic curves in class 3330k do not have complex multiplication.

Modular form 3330.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - 3 q^{11} + 2 q^{13} + q^{14} + q^{16} - 3 q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.