Properties

Label 75348c
Number of curves $2$
Conductor $75348$
CM no
Rank $2$
Graph

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

Elliptic curves in class 75348c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75348.g2 75348c1 \([0, 0, 0, -1980, 33777]\) \(73598976000/336973\) \(3930453072\) \([2]\) \(46080\) \(0.69188\) \(\Gamma_0(N)\)-optimal
75348.g1 75348c2 \([0, 0, 0, -3015, -5346]\) \(16241202000/9332687\) \(1741703378688\) \([2]\) \(92160\) \(1.0385\)  

Rank

sage: E.rank()
 

The elliptic curves in class 75348c have rank \(2\).

Complex multiplication

The elliptic curves in class 75348c do not have complex multiplication.

Modular form 75348.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{7} - q^{13} - 6q^{17} - 4q^{19} + O(q^{20})\)  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.