Properties

Label 1950.t
Number of curves $2$
Conductor $1950$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1950.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.t1 1950o2 \([1, 1, 1, -3363, -76479]\) \(-168256703745625/30371328\) \(-759283200\) \([]\) \(1944\) \(0.70771\)  
1950.t2 1950o1 \([1, 1, 1, 12, -339]\) \(7604375/2047032\) \(-51175800\) \([]\) \(648\) \(0.15840\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1950.t have rank \(0\).

Complex multiplication

The elliptic curves in class 1950.t do not have complex multiplication.

Modular form 1950.2.a.t

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.