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SageMath
E = EllipticCurve("gf1")
E.isogeny_class()
Elliptic curves in class 466578gf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 466578.gf2 | 466578gf1 | \([1, -1, 1, -29438156, -82559570481]\) | \(-5999796014211/2790817792\) | \(-1312352501417215001985024\) | \([]\) | \(133816320\) | \(3.3340\) | \(\Gamma_0(N)\)-optimal |
| 466578.gf1 | 466578gf2 | \([1, -1, 1, -2604948716, -51173057938481]\) | \(-5702623460245179/252448\) | \(-86540317268586692694624\) | \([]\) | \(401448960\) | \(3.8833\) |
Rank
sage: E.rank()
The elliptic curves in class 466578gf have rank \(0\).
Complex multiplication
The elliptic curves in class 466578gf do not have complex multiplication.Modular form 466578.2.a.gf
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.
