Properties

Label 92400hp
Number of curves $4$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("hp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400hp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.hk4 92400hp1 \([0, 1, 0, -1263008, -37752012]\) \(3481467828171481/2005331497785\) \(128341215858240000000\) \([2]\) \(2949120\) \(2.5480\) \(\Gamma_0(N)\)-optimal
92400.hk2 92400hp2 \([0, 1, 0, -14385008, -20954220012]\) \(5143681768032498601/14238434358225\) \(911259798926400000000\) \([2, 2]\) \(5898240\) \(2.8946\)  
92400.hk3 92400hp3 \([0, 1, 0, -8715008, -37635360012]\) \(-1143792273008057401/8897444448004035\) \(-569436444672258240000000\) \([2]\) \(11796480\) \(3.2412\)  
92400.hk1 92400hp4 \([0, 1, 0, -230007008, -1342717080012]\) \(21026497979043461623321/161783881875\) \(10354168440000000000\) \([2]\) \(11796480\) \(3.2412\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92400hp have rank \(1\).

Complex multiplication

The elliptic curves in class 92400hp do not have complex multiplication.

Modular form 92400.2.a.hp

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} + q^{11} - 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.