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Properties

Label 3330ba
Number of curves $2$
Conductor $3330$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 3330ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3330.u2 3330ba1 \([1, -1, 1, 1138, 40061]\) \(223759095911/1094104800\) \(-797602399200\) \([]\) \(5760\) \(0.96602\) \(\Gamma_0(N)\)-optimal
3330.u1 3330ba2 \([1, -1, 1, -63797, 6225869]\) \(-39390416456458249/56832000000\) \(-41430528000000\) \([3]\) \(17280\) \(1.5153\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3330ba have rank \(1\).

Complex multiplication

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

Modular form 3330.2.a.ba

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