Properties

Label 369600.mh
Number of curves $4$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("mh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.mh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.mh1 369600mh3 \([0, 1, 0, -14901633, -21906511137]\) \(89343998142858649/1112702976000\) \(4557631389696000000000\) \([2]\) \(23887872\) \(2.9657\)  
369600.mh2 369600mh4 \([0, 1, 0, -2613633, -56939599137]\) \(-482056280171929/341652696000000\) \(-1399409442816000000000000\) \([2]\) \(47775744\) \(3.3122\)  
369600.mh3 369600mh1 \([0, 1, 0, -1437633, 647272863]\) \(80224711835689/2173469760\) \(8902532136960000000\) \([2]\) \(7962624\) \(2.4164\) \(\Gamma_0(N)\)-optimal
369600.mh4 369600mh2 \([0, 1, 0, 290367, 2107432863]\) \(661003929431/468755040600\) \(-1920020646297600000000\) \([2]\) \(15925248\) \(2.7629\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600.mh have rank \(0\).

Complex multiplication

The elliptic curves in class 369600.mh do not have complex multiplication.

Modular form 369600.2.a.mh

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.