Properties

Label 25200.eh
Number of curves $8$
Conductor $25200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("eh1")
 
E.isogeny_class()
 

Elliptic curves in class 25200.eh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.eh1 25200eg8 \([0, 0, 0, -1264437075, -17305890272750]\) \(4791901410190533590281/41160000\) \(1920360960000000000\) \([2]\) \(5308416\) \(3.5494\)  
25200.eh2 25200eg6 \([0, 0, 0, -79029075, -270391904750]\) \(1169975873419524361/108425318400\) \(5058691655270400000000\) \([2, 2]\) \(2654208\) \(3.2029\)  
25200.eh3 25200eg7 \([0, 0, 0, -73269075, -311477984750]\) \(-932348627918877961/358766164249920\) \(-16738594159244267520000000\) \([2]\) \(5308416\) \(3.5494\)  
25200.eh4 25200eg5 \([0, 0, 0, -15687075, -23494022750]\) \(9150443179640281/184570312500\) \(8611312500000000000000\) \([2]\) \(1769472\) \(3.0001\)  
25200.eh5 25200eg3 \([0, 0, 0, -5301075, -3570272750]\) \(353108405631241/86318776320\) \(4027288827985920000000\) \([2]\) \(1327104\) \(2.8563\)  
25200.eh6 25200eg2 \([0, 0, 0, -2079075, 605745250]\) \(21302308926361/8930250000\) \(416649744000000000000\) \([2, 2]\) \(884736\) \(2.6536\)  
25200.eh7 25200eg1 \([0, 0, 0, -1791075, 922257250]\) \(13619385906841/6048000\) \(282175488000000000\) \([2]\) \(442368\) \(2.3070\) \(\Gamma_0(N)\)-optimal
25200.eh8 25200eg4 \([0, 0, 0, 6920925, 4448745250]\) \(785793873833639/637994920500\) \(-29766291010848000000000\) \([2]\) \(1769472\) \(3.0001\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25200.eh have rank \(0\).

Complex multiplication

The elliptic curves in class 25200.eh do not have complex multiplication.

Modular form 25200.2.a.eh

sage: E.q_eigenform(10)
 
\(q + q^{7} - 2 q^{13} - 6 q^{17} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.