Properties

Label 75456.c
Number of curves $2$
Conductor $75456$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 75456.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75456.c1 75456dk2 \([0, 0, 0, -83244, -7847984]\) \(333822098953/53954184\) \(10310805130051584\) \([]\) \(700416\) \(1.7948\)  
75456.c2 75456dk1 \([0, 0, 0, -22764, 1320784]\) \(6826561273/7074\) \(1351862452224\) \([]\) \(233472\) \(1.2455\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 75456.c have rank \(2\).

Complex multiplication

The elliptic curves in class 75456.c do not have complex multiplication.

Modular form 75456.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.