Properties

 Label 720.c Number of curves 8 Conductor 720 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("720.c1")

sage: E.isogeny_class()

Elliptic curves in class 720.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
720.c1 720h7 [0, 0, 0, -311043, -66769598] [2] 2048
720.c2 720h5 [0, 0, 0, -19443, -1042958] [2, 2] 1024
720.c3 720h8 [0, 0, 0, -15843, -1441118] [2] 2048
720.c4 720h4 [0, 0, 0, -11523, 476098] [2] 512
720.c5 720h3 [0, 0, 0, -1443, -9758] [2, 2] 512
720.c6 720h2 [0, 0, 0, -723, 7378] [2, 2] 256
720.c7 720h1 [0, 0, 0, -3, 322] [2] 128 $$\Gamma_0(N)$$-optimal
720.c8 720h6 [0, 0, 0, 5037, -73262] [2] 1024

Rank

sage: E.rank()

The elliptic curves in class 720.c have rank $$1$$.

Modular form720.2.a.c

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.