# Properties

 Label 99450.dq Number of curves 8 Conductor 99450 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("99450.dq1")

sage: E.isogeny_class()

## Elliptic curves in class 99450.dq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
99450.dq1 99450cr8 [1, -1, 1, -1482975001355, 695102884051264647] [2] 637009920
99450.dq2 99450cr6 [1, -1, 1, -92685938855, 10860999629389647] [2, 2] 318504960
99450.dq3 99450cr7 [1, -1, 1, -92517868355, 10902350686786647] [2] 637009920
99450.dq4 99450cr5 [1, -1, 1, -18308984855, 953434712977647] [2] 212336640
99450.dq5 99450cr3 [1, -1, 1, -5803376855, 169057784545647] [2] 159252480
99450.dq6 99450cr2 [1, -1, 1, -1250384855, 11970578977647] [2, 2] 106168320
99450.dq7 99450cr1 [1, -1, 1, -471632855, -3796034014353] [2] 53084160 $$\Gamma_0(N)$$-optimal
99450.dq8 99450cr4 [1, -1, 1, 3348183145, 79560331441647] [2] 212336640

## Rank

sage: E.rank()

The elliptic curves in class 99450.dq have rank $$0$$.

## Modular form 99450.2.a.dq

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 4q^{7} + q^{8} - q^{13} + 4q^{14} + q^{16} + q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.