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Properties

Label 308763.x
Number of curves $2$
Conductor $308763$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 308763.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308763.x1 308763x2 \([1, -1, 0, -235026, -43796453]\) \(408023180713/1421\) \(5000134884381\) \([2]\) \(1327104\) \(1.6561\)  
308763.x2 308763x1 \([1, -1, 0, -14481, -701960]\) \(-95443993/5887\) \(-20714844521007\) \([2]\) \(663552\) \(1.3096\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 308763.x have rank \(1\).

Complex multiplication

The elliptic curves in class 308763.x do not have complex multiplication.

Modular form 308763.2.a.x

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