Properties

Label 338130.t
Number of curves $2$
Conductor $338130$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 338130.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
338130.t1 338130t1 \([1, -1, 0, -13722930, -14998822700]\) \(3305951312273/788486400\) \(68165092382795058643200\) \([2]\) \(46792704\) \(3.0927\) \(\Gamma_0(N)\)-optimal
338130.t2 338130t2 \([1, -1, 0, 32262750, -94084995164]\) \(42959580557167/69087330000\) \(-5972638503252115114290000\) \([2]\) \(93585408\) \(3.4393\)  

Rank

sage: E.rank()
 

The elliptic curves in class 338130.t have rank \(1\).

Complex multiplication

The elliptic curves in class 338130.t do not have complex multiplication.

Modular form 338130.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + 2 q^{7} - q^{8} + q^{10} - 6 q^{11} + q^{13} - 2 q^{14} + q^{16} - 4 q^{19} + O(q^{20})\) 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.