Properties

Label 62400.m
Number of curves $4$
Conductor $62400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62400.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.m1 62400ff4 \([0, -1, 0, -22752033, -41750856063]\) \(2543984126301795848/909361981125\) \(465593334336000000000\) \([2]\) \(4718592\) \(2.9351\)  
62400.m2 62400ff3 \([0, -1, 0, -11752033, 15191643937]\) \(350584567631475848/8259273550125\) \(4228748057664000000000\) \([4]\) \(4718592\) \(2.9351\)  
62400.m3 62400ff2 \([0, -1, 0, -1627033, -451481063]\) \(7442744143086784/2927948765625\) \(187388721000000000000\) \([2, 2]\) \(2359296\) \(2.5885\)  
62400.m4 62400ff1 \([0, -1, 0, 326092, -51090438]\) \(3834800837445824/3342041015625\) \(-3342041015625000000\) \([2]\) \(1179648\) \(2.2419\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62400.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{7} + q^{9} + q^{13} - 2q^{17} - 8q^{19} + O(q^{20})\)  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.