Properties

Label 62400.o
Number of curves $2$
Conductor $62400$
CM no
Rank $1$
Graph

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

Elliptic curves in class 62400.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.o1 62400fe2 \([0, -1, 0, -215233, 38511457]\) \(-168256703745625/30371328\) \(-199041535180800\) \([]\) \(373248\) \(1.7474\)  
62400.o2 62400fe1 \([0, -1, 0, 767, 175777]\) \(7604375/2047032\) \(-13415428915200\) \([]\) \(124416\) \(1.1981\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 62400.o have rank \(1\).

Complex multiplication

The elliptic curves in class 62400.o do not have complex multiplication.

Modular form 62400.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{7} + q^{9} + q^{13} + 5q^{19} + O(q^{20})\)  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.