Properties

Label 4950.u
Number of curves $2$
Conductor $4950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 4950.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4950.u1 4950p2 \([1, -1, 0, -207, 1381]\) \(-53969305/10648\) \(-194059800\) \([]\) \(2592\) \(0.31338\)  
4950.u2 4950p1 \([1, -1, 0, 18, -14]\) \(34295/22\) \(-400950\) \([]\) \(864\) \(-0.23592\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4950.u have rank \(1\).

Complex multiplication

The elliptic curves in class 4950.u do not have complex multiplication.

Modular form 4950.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 4 q^{7} - q^{8} + q^{11} - 5 q^{13} - 4 q^{14} + q^{16} - 7 q^{19} + O(q^{20})\) 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.