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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 78400fn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.bj2 | 78400fn1 | \([0, 1, 0, 8167, 828463]\) | \(1280/7\) | \(-329417200000000\) | \([]\) | \(276480\) | \(1.4678\) | \(\Gamma_0(N)\)-optimal |
| 78400.bj1 | 78400fn2 | \([0, 1, 0, -481833, 128718463]\) | \(-262885120/343\) | \(-16141442800000000\) | \([]\) | \(829440\) | \(2.0171\) |
Rank
sage: E.rank()
The elliptic curves in class 78400fn have rank \(1\).
Complex multiplication
The elliptic curves in class 78400fn do not have complex multiplication.Modular form 78400.2.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.
