Properties

Label 3465.g
Number of curves $4$
Conductor $3465$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 3465.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3465.g1 3465t3 \([1, -1, 1, -19112, 1010724]\) \(1058993490188089/13182390375\) \(9609962583375\) \([4]\) \(9216\) \(1.3009\)  
3465.g2 3465t2 \([1, -1, 1, -2237, -15276]\) \(1697509118089/833765625\) \(607815140625\) \([2, 2]\) \(4608\) \(0.95433\)  
3465.g3 3465t1 \([1, -1, 1, -1832, -29694]\) \(932288503609/779625\) \(568346625\) \([2]\) \(2304\) \(0.60776\) \(\Gamma_0(N)\)-optimal
3465.g4 3465t4 \([1, -1, 1, 8158, -123384]\) \(82375335041831/56396484375\) \(-41113037109375\) \([2]\) \(9216\) \(1.3009\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3465.g have rank \(1\).

Complex multiplication

The elliptic curves in class 3465.g do not have complex multiplication.

Modular form 3465.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} + q^{7} + 3 q^{8} - q^{10} + q^{11} - 2 q^{13} - q^{14} - q^{16} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.