Properties

Label 176400sd
Number of curves $2$
Conductor $176400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("sd1")
 
E.isogeny_class()
 

Elliptic curves in class 176400sd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.sm2 176400sd1 \([0, 0, 0, -165375, -57881250]\) \(-432\) \(-1157842633500000000\) \([2]\) \(2211840\) \(2.1545\) \(\Gamma_0(N)\)-optimal
176400.sm1 176400sd2 \([0, 0, 0, -3472875, -2488893750]\) \(1000188\) \(4631370534000000000\) \([2]\) \(4423680\) \(2.5010\)  

Rank

sage: E.rank()
 

The elliptic curves in class 176400sd have rank \(1\).

Complex multiplication

The elliptic curves in class 176400sd do not have complex multiplication.

Modular form 176400.2.a.sd

sage: E.q_eigenform(10)
 
\(q + 4 q^{11} + 4 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 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.