Properties

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

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 311696bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
311696.bl2 311696bl1 \([0, 0, 0, -15851, 3575066]\) \(-60698457/725788\) \(-5266545520918528\) \([2]\) \(1474560\) \(1.6985\) \(\Gamma_0(N)\)-optimal
311696.bl1 311696bl2 \([0, 0, 0, -461131, 120149370]\) \(1494447319737/5411854\) \(39270111166849024\) \([2]\) \(2949120\) \(2.0451\)  

Rank

sage: E.rank()
 

The elliptic curves in class 311696bl have rank \(2\).

Complex multiplication

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

Modular form 311696.2.a.bl

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + q^{7} - 3 q^{9} - 4 q^{13} + 8 q^{17} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.