Properties

Label 47096.b
Number of curves $2$
Conductor $47096$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47096.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.b1 47096l2 \([0, 1, 0, -33920, -2386976]\) \(3543122/49\) \(59691709908992\) \([2]\) \(200704\) \(1.4490\)  
47096.b2 47096l1 \([0, 1, 0, -280, -99456]\) \(-4/7\) \(-4263693564928\) \([2]\) \(100352\) \(1.1024\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47096.b have rank \(1\).

Complex multiplication

The elliptic curves in class 47096.b do not have complex multiplication.

Modular form 47096.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - 4q^{5} + q^{7} + q^{9} + 8q^{15} + 2q^{17} + 2q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.