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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 46800fn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.fj2 | 46800fn1 | \([0, 0, 0, 43125, -74263750]\) | \(7604375/2047032\) | \(-2387658124800000000\) | \([]\) | \(622080\) | \(2.2056\) | \(\Gamma_0(N)\)-optimal |
| 46800.fj1 | 46800fn2 | \([0, 0, 0, -12106875, -16216753750]\) | \(-168256703745625/30371328\) | \(-35425116979200000000\) | \([]\) | \(1866240\) | \(2.7549\) |
Rank
sage: E.rank()
The elliptic curves in class 46800fn have rank \(1\).
Complex multiplication
The elliptic curves in class 46800fn do not have complex multiplication.Modular form 46800.2.a.fn
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
