Properties

Label 289800e
Number of curves $2$
Conductor $289800$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 289800e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
289800.e1 289800e1 \([0, 0, 0, -2175, -10750]\) \(10536048/5635\) \(608580000000\) \([2]\) \(368640\) \(0.95246\) \(\Gamma_0(N)\)-optimal
289800.e2 289800e2 \([0, 0, 0, 8325, -84250]\) \(147704148/92575\) \(-39992400000000\) \([2]\) \(737280\) \(1.2990\)  

Rank

sage: E.rank()
 

The elliptic curves in class 289800e have rank \(2\).

Complex multiplication

The elliptic curves in class 289800e do not have complex multiplication.

Modular form 289800.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.