Properties

Label 4950t
Number of curves $3$
Conductor $4950$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4950t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4950.q2 4950t1 \([1, -1, 0, -252, 1606]\) \(-19465109/22\) \(-2004750\) \([]\) \(1440\) \(0.12300\) \(\Gamma_0(N)\)-optimal
4950.q3 4950t2 \([1, -1, 0, 1773, -16619]\) \(6761990971/5153632\) \(-469624716000\) \([]\) \(7200\) \(0.92772\)  
4950.q1 4950t3 \([1, -1, 0, -272952, -54820544]\) \(-24680042791780949/369098752\) \(-33634123776000\) \([]\) \(36000\) \(1.7324\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4950.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{7} - q^{8} - q^{11} + 4 q^{13} - 3 q^{14} + q^{16} - 3 q^{17} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.