Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 311696d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
311696.d2 311696d1 \([0, 1, 0, -124159229, -532492771538]\) \(5610564864985137152/548176896967\) \(20681159175406120851152\) \([2]\) \(39029760\) \(3.3174\) \(\Gamma_0(N)\)-optimal
311696.d1 311696d2 \([0, 1, 0, -1986501084, -34079229074024]\) \(1436203562785124669552/13712209\) \(8277163916815211264\) \([2]\) \(78059520\) \(3.6640\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 311696.2.a.d

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