Properties

 Label 4900.m Number of curves $2$ Conductor $4900$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

Elliptic curves in class 4900.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4900.m1 4900p1 $$[0, 0, 0, -98000, 11790625]$$ $$28311552/49$$ $$180150031250000$$ $$[2]$$ $$17280$$ $$1.6293$$ $$\Gamma_0(N)$$-optimal
4900.m2 4900p2 $$[0, 0, 0, -67375, 19293750]$$ $$-574992/2401$$ $$-141237624500000000$$ $$[2]$$ $$34560$$ $$1.9759$$

Rank

sage: E.rank()

The elliptic curves in class 4900.m have rank $$0$$.

Complex multiplication

The elliptic curves in class 4900.m do not have complex multiplication.

Modular form4900.2.a.m

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.