Properties

Label 1950.o
Number of curves $4$
Conductor $1950$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1950.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.o1 1950n4 \([1, 1, 1, -21814438, -39224901469]\) \(73474353581350183614361/576510977802240\) \(9007984028160000000\) \([2]\) \(103680\) \(2.8101\)  
1950.o2 1950n3 \([1, 1, 1, -1334438, -640581469]\) \(-16818951115904497561/1592332281446400\) \(-24880191897600000000\) \([2]\) \(51840\) \(2.4635\)  
1950.o3 1950n2 \([1, 1, 1, -400063, 3499781]\) \(453198971846635561/261896250564000\) \(4092128915062500000\) \([2]\) \(34560\) \(2.2608\)  
1950.o4 1950n1 \([1, 1, 1, 99937, 499781]\) \(7064514799444439/4094064000000\) \(-63969750000000000\) \([2]\) \(17280\) \(1.9142\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1950.2.a.o

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.