Properties

Label 481338t
Number of curves $2$
Conductor $481338$
CM no
Rank $1$
Graph

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

Elliptic curves in class 481338t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
481338.t1 481338t1 \([1, -1, 0, -3289347, -2087747051]\) \(3047678972871625/304559880768\) \(393329330654331120192\) \([2]\) \(20643840\) \(2.6881\) \(\Gamma_0(N)\)-optimal
481338.t2 481338t2 \([1, -1, 0, 4072293, -10110462323]\) \(5783051584712375/37533175779528\) \(-48472894294107017938632\) \([2]\) \(41287680\) \(3.0347\)  

Rank

sage: E.rank()
 

The elliptic curves in class 481338t have rank \(1\).

Complex multiplication

The elliptic curves in class 481338t do not have complex multiplication.

Modular form 481338.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{7} - q^{8} - q^{13} + 2 q^{14} + q^{16} - q^{17} - 4 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.