Properties

 Label 9408.h Number of curves $6$ Conductor $9408$ CM no Rank $2$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

Elliptic curves in class 9408.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.h1 9408q5 $$[0, -1, 0, -75329, 7982913]$$ $$3065617154/9$$ $$138784407552$$ $$[2]$$ $$24576$$ $$1.3673$$
9408.h2 9408q3 $$[0, -1, 0, -12609, -540735]$$ $$28756228/3$$ $$23130734592$$ $$[2]$$ $$12288$$ $$1.0208$$
9408.h3 9408q4 $$[0, -1, 0, -4769, 122529]$$ $$1556068/81$$ $$624529833984$$ $$[2, 2]$$ $$12288$$ $$1.0208$$
9408.h4 9408q2 $$[0, -1, 0, -849, -6831]$$ $$35152/9$$ $$17348050944$$ $$[2, 2]$$ $$6144$$ $$0.67418$$
9408.h5 9408q1 $$[0, -1, 0, 131, -755]$$ $$2048/3$$ $$-361417728$$ $$[2]$$ $$3072$$ $$0.32760$$ $$\Gamma_0(N)$$-optimal
9408.h6 9408q6 $$[0, -1, 0, 3071, 478465]$$ $$207646/6561$$ $$-101173833105408$$ $$[2]$$ $$24576$$ $$1.3673$$

Rank

sage: E.rank()

The elliptic curves in class 9408.h have rank $$2$$.

Complex multiplication

The elliptic curves in class 9408.h do not have complex multiplication.

Modular form9408.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} + q^{9} - 4q^{11} - 2q^{13} + 2q^{15} - 2q^{17} - 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.