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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 58800fm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.dt2 | 58800fm1 | \([0, -1, 0, -933, 12237]\) | \(-28672/3\) | \(-9408000000\) | \([]\) | \(30720\) | \(0.65278\) | \(\Gamma_0(N)\)-optimal |
58800.dt1 | 58800fm2 | \([0, -1, 0, -364933, -84799763]\) | \(-1713910976512/1594323\) | \(-4999796928000000\) | \([]\) | \(399360\) | \(1.9353\) |
Rank
sage: E.rank()
The elliptic curves in class 58800fm have rank \(1\).
Complex multiplication
The elliptic curves in class 58800fm do not have complex multiplication.Modular form 58800.2.a.fm
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.