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Properties

Label 471900p
Number of curves $2$
Conductor $471900$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("p1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 471900p have rank \(1\).

Complex multiplication

The elliptic curves in class 471900p do not have complex multiplication.

Modular form 471900.2.a.p

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} + q^{9} - q^{13} - 2 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 471900p

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
471900.p1 471900p1 \([0, -1, 0, -246033, -4422438]\) \(3718856704/2132325\) \(944385952331250000\) \([2]\) \(4976640\) \(2.1388\) \(\Gamma_0(N)\)-optimal
471900.p2 471900p2 \([0, -1, 0, 979092, -36275688]\) \(14647977776/8555625\) \(-60627246322500000000\) \([2]\) \(9953280\) \(2.4854\)