Properties

Label 31200.cb
Number of curves $4$
Conductor $31200$
CM no
Rank $0$
Graph

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

Elliptic curves in class 31200.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.cb1 31200n4 \([0, 1, 0, -93608, -11054712]\) \(11339065490696/351\) \(2808000000\) \([2]\) \(98304\) \(1.3174\)  
31200.cb2 31200n3 \([0, 1, 0, -9233, 45663]\) \(1360251712/771147\) \(49353408000000\) \([2]\) \(98304\) \(1.3174\)  
31200.cb3 31200n1 \([0, 1, 0, -5858, -173712]\) \(22235451328/123201\) \(123201000000\) \([2, 2]\) \(49152\) \(0.97086\) \(\Gamma_0(N)\)-optimal
31200.cb4 31200n2 \([0, 1, 0, -2608, -362212]\) \(-245314376/6908733\) \(-55269864000000\) \([2]\) \(98304\) \(1.3174\)  

Rank

sage: E.rank()
 

The elliptic curves in class 31200.cb have rank \(0\).

Complex multiplication

The elliptic curves in class 31200.cb do not have complex multiplication.

Modular form 31200.2.a.cb

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + 4q^{11} - q^{13} + 6q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.