Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 28224o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28224.eo1 | 28224o1 | \([0, 0, 0, -10584, 370440]\) | \(55296/7\) | \(16598831993856\) | \([2]\) | \(73728\) | \(1.2659\) | \(\Gamma_0(N)\)-optimal |
28224.eo2 | 28224o2 | \([0, 0, 0, 15876, 1926288]\) | \(11664/49\) | \(-1859069183311872\) | \([2]\) | \(147456\) | \(1.6125\) |
Rank
sage: E.rank()
The elliptic curves in class 28224o have rank \(0\).
Complex multiplication
The elliptic curves in class 28224o do not have complex multiplication.Modular form 28224.2.a.o
sage: E.q_eigenform(10)
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 Cremona 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 Cremona labels.