Properties

Label 235340c
Number of curves $2$
Conductor $235340$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 235340c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235340.c2 235340c1 \([0, 1, 0, 22974, -50332751]\) \(10496/8575\) \(-1095531741435401200\) \([3]\) \(2851632\) \(2.1405\) \(\Gamma_0(N)\)-optimal
235340.c1 235340c2 \([0, 1, 0, -9625966, -11499764955]\) \(-772086379264/109375\) \(-13973619150961750000\) \([]\) \(8554896\) \(2.6898\)  

Rank

sage: E.rank()
 

The elliptic curves in class 235340c have rank \(0\).

Complex multiplication

The elliptic curves in class 235340c do not have complex multiplication.

Modular form 235340.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + q^{7} + q^{9} - 3 q^{11} - 4 q^{13} + 2 q^{15} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.