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Properties

Label 1334.a
Number of curves $2$
Conductor $1334$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1334.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1334.a1 1334b2 \([1, -1, 0, -8717, -310165]\) \(73257631680515625/248996365298\) \(248996365298\) \([2]\) \(1920\) \(1.0505\)  
1334.a2 1334b1 \([1, -1, 0, -307, -9087]\) \(-3205784543625/34421951708\) \(-34421951708\) \([2]\) \(960\) \(0.70391\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1334.a have rank \(0\).

Complex multiplication

The elliptic curves in class 1334.a do not have complex multiplication.

Modular form 1334.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 4 q^{7} - q^{8} - 3 q^{9} + 2 q^{11} + 6 q^{13} - 4 q^{14} + q^{16} + 2 q^{17} + 3 q^{18} - 2 q^{19} + O(q^{20})\) 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 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.