Properties

Label 311696f
Number of curves $2$
Conductor $311696$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 311696f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
311696.f2 311696f1 \([0, 1, 0, -7784, 240436]\) \(7189057/644\) \(4673066123264\) \([2]\) \(622080\) \(1.1708\) \(\Gamma_0(N)\)-optimal
311696.f1 311696f2 \([0, 1, 0, -27144, -1455500]\) \(304821217/51842\) \(376181822922752\) \([2]\) \(1244160\) \(1.5174\)  

Rank

sage: E.rank()
 

The elliptic curves in class 311696f have rank \(0\).

Complex multiplication

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

Modular form 311696.2.a.f

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