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Properties

Label 47190.t
Number of curves $2$
Conductor $47190$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 47190.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.t1 47190bd2 \([1, 0, 1, -347129764, -2498968244038]\) \(-21580315425730848803929/96405029296875000\) \(-20665274202850341796875000\) \([]\) \(25660800\) \(3.7097\)  
47190.t2 47190bd1 \([1, 0, 1, 10263701, -18127813684]\) \(557820238477845431/985142146218750\) \(-211173968089389631218750\) \([3]\) \(8553600\) \(3.1604\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 47190.t have rank \(0\).

Complex multiplication

The elliptic curves in class 47190.t do not have complex multiplication.

Modular form 47190.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} + q^{12} + q^{13} + 4 q^{14} - q^{15} + q^{16} - q^{18} - q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.