Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3450.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.c1 3450a2 \([1, 1, 0, -19650, -742500]\) \(53706380371489/16171875000\) \(252685546875000\) \([2]\) \(11520\) \(1.4688\)  
3450.c2 3450a1 \([1, 1, 0, 3350, -75500]\) \(265971760991/317400000\) \(-4959375000000\) \([2]\) \(5760\) \(1.1222\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3450.2.a.c

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