Properties

 Label 660.c Number of curves $4$ Conductor $660$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 660.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
660.c1 660c4 $$[0, 1, 0, -1556, -13356]$$ $$1628514404944/664335375$$ $$170069856000$$ $$$$ $$864$$ $$0.85261$$
660.c2 660c2 $$[0, 1, 0, -716, 7140]$$ $$158792223184/16335$$ $$4181760$$ $$$$ $$288$$ $$0.30330$$
660.c3 660c1 $$[0, 1, 0, -41, 120]$$ $$-488095744/200475$$ $$-3207600$$ $$$$ $$144$$ $$-0.043272$$ $$\Gamma_0(N)$$-optimal
660.c4 660c3 $$[0, 1, 0, 319, -1356]$$ $$223673040896/187171875$$ $$-2994750000$$ $$$$ $$432$$ $$0.50603$$

Rank

sage: E.rank()

The elliptic curves in class 660.c have rank $$1$$.

Complex multiplication

The elliptic curves in class 660.c do not have complex multiplication.

Modular form660.2.a.c

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 4 q^{7} + q^{9} - q^{11} - 4 q^{13} - q^{15} - 6 q^{17} + 2 q^{19} + O(q^{20})$$ 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 