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Properties

Label 3450.i
Number of curves $2$
Conductor $3450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 3450.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.i1 3450l2 \([1, 0, 1, -66701, -4248952]\) \(84013940106985/28705554432\) \(11213107200000000\) \([]\) \(25920\) \(1.7817\)  
3450.i2 3450l1 \([1, 0, 1, -27326, 1736048]\) \(5776556465785/1073088\) \(419175000000\) \([3]\) \(8640\) \(1.2324\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3450.i have rank \(1\).

Complex multiplication

The elliptic curves in class 3450.i do not have complex multiplication.

Modular form 3450.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - 3 q^{11} + q^{12} - q^{13} + q^{14} + q^{16} + 6 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.