Properties

Label 342.a
Number of curves $2$
Conductor $342$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 342.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
342.a1 342e2 \([1, -1, 0, -33, -65]\) \(149721291/722\) \(19494\) \([2]\) \(32\) \(-0.32819\)  
342.a2 342e1 \([1, -1, 0, -3, 1]\) \(132651/76\) \(2052\) \([2]\) \(16\) \(-0.67476\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 342.a have rank \(1\).

Complex multiplication

The elliptic curves in class 342.a do not have complex multiplication.

Modular form 342.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.