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Properties

Label 17325t
Number of curves $2$
Conductor $17325$
CM no
Rank $1$
Graph

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

Elliptic curves in class 17325t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17325.l2 17325t1 \([1, -1, 1, -5, -23628]\) \(-1/21175\) \(-241196484375\) \([2]\) \(18432\) \(0.86296\) \(\Gamma_0(N)\)-optimal
17325.l1 17325t2 \([1, -1, 1, -12380, -518628]\) \(18420660721/336875\) \(3837216796875\) \([2]\) \(36864\) \(1.2095\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17325t have rank \(1\).

Complex multiplication

The elliptic curves in class 17325t do not have complex multiplication.

Modular form 17325.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{7} + 3 q^{8} + q^{11} - 4 q^{13} + q^{14} - q^{16} - 4 q^{17} - 8 q^{19} + O(q^{20})\) 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 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.