Properties

Label 311696j
Number of curves $2$
Conductor $311696$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 311696j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
311696.j2 311696j1 \([0, 1, 0, -11578288, -53325652140]\) \(-23655968592999625/155579103523228\) \(-1128930804599657754247168\) \([2]\) \(33177600\) \(3.2987\) \(\Gamma_0(N)\)-optimal
311696.j1 311696j2 \([0, 1, 0, -295028048, -1946429909228]\) \(391379047744832043625/964051690355138\) \(6995461638624209430192128\) \([2]\) \(66355200\) \(3.6453\)  

Rank

sage: E.rank()
 

The elliptic curves in class 311696j have rank \(1\).

Complex multiplication

The elliptic curves in class 311696j do not have complex multiplication.

Modular form 311696.2.a.j

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{7} + q^{9} + 2 q^{17} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.