Show commands:
SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 176400eo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.fr1 | 176400eo1 | \([0, 0, 0, -474075, -125637750]\) | \(-5154200289/20\) | \(-45722880000000\) | \([]\) | \(967680\) | \(1.8343\) | \(\Gamma_0(N)\)-optimal |
176400.fr2 | 176400eo2 | \([0, 0, 0, 3305925, 1192070250]\) | \(1747829720511/1280000000\) | \(-2926264320000000000000\) | \([]\) | \(6773760\) | \(2.8073\) |
Rank
sage: E.rank()
The elliptic curves in class 176400eo have rank \(0\).
Complex multiplication
The elliptic curves in class 176400eo do not have complex multiplication.Modular form 176400.2.a.eo
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.