Properties

Label 31200.c
Number of curves $2$
Conductor $31200$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31200.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.c1 31200bp1 \([0, -1, 0, -72558, -7496388]\) \(42246001231552/14414517\) \(14414517000000\) \([2]\) \(98304\) \(1.4965\) \(\Gamma_0(N)\)-optimal
31200.c2 31200bp2 \([0, -1, 0, -62433, -9673263]\) \(-420526439488/390971529\) \(-25022177856000000\) \([2]\) \(196608\) \(1.8431\)  

Rank

sage: E.rank()
 

The elliptic curves in class 31200.c have rank \(1\).

Complex multiplication

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

Modular form 31200.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{7} + q^{9} - 2q^{11} + q^{13} - 6q^{17} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.