Properties

Label 317889t
Number of curves $2$
Conductor $317889$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 317889t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
317889.t2 317889t1 \([0, 0, 1, -552630, 170463582]\) \(-5304438784000/497763387\) \(-1751501812460478507\) \([]\) \(3369600\) \(2.2426\) \(\Gamma_0(N)\)-optimal
317889.t1 317889t2 \([0, 0, 1, -45726330, 119013885279]\) \(-3004935183806464000/2037123\) \(-7168113846639603\) \([]\) \(10108800\) \(2.7920\)  

Rank

sage: E.rank()
 

The elliptic curves in class 317889t have rank \(1\).

Complex multiplication

The elliptic curves in class 317889t do not have complex multiplication.

Modular form 317889.2.a.t

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - 2 q^{7} + q^{11} + 4 q^{16} - 3 q^{17} - q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.