Properties

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

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 62400.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.bm1 62400m2 \([0, -1, 0, -428033, -75384063]\) \(4234737878642/1247410125\) \(2554695936000000000\) \([2]\) \(737280\) \(2.2378\)  
62400.bm2 62400m1 \([0, -1, 0, 71967, -7884063]\) \(40254822716/49359375\) \(-50544000000000000\) \([2]\) \(368640\) \(1.8913\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62400.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} + q^{9} - 4 q^{11} - q^{13} - 2 q^{19} + O(q^{20})\) 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.