Properties

Label 193200.cb
Number of curves $2$
Conductor $193200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 193200.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.cb1 193200dq2 \([0, -1, 0, -3671008, -630495488]\) \(85486955243540761/46777901234400\) \(2993785679001600000000\) \([2]\) \(7372800\) \(2.8116\)  
193200.cb2 193200dq1 \([0, -1, 0, -2199008, 1247776512]\) \(18374873741826841/136564270080\) \(8740113285120000000\) \([2]\) \(3686400\) \(2.4651\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 193200.cb have rank \(1\).

Complex multiplication

The elliptic curves in class 193200.cb do not have complex multiplication.

Modular form 193200.2.a.cb

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - 2 q^{11} + 2 q^{13} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.