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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 145600eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145600.w4 | 145600eu1 | \([0, 1, 0, -373633, 87664863]\) | \(1408317602329/2153060\) | \(8818933760000000\) | \([2]\) | \(1327104\) | \(1.9593\) | \(\Gamma_0(N)\)-optimal |
| 145600.w3 | 145600eu2 | \([0, 1, 0, -485633, 30656863]\) | \(3092354182009/1689383150\) | \(6919713382400000000\) | \([2]\) | \(2654208\) | \(2.3059\) | |
| 145600.w2 | 145600eu3 | \([0, 1, 0, -1517633, -634407137]\) | \(94376601570889/12235496000\) | \(50116591616000000000\) | \([2]\) | \(3981312\) | \(2.5086\) | |
| 145600.w1 | 145600eu4 | \([0, 1, 0, -23469633, -43770087137]\) | \(349046010201856969/7245875000\) | \(29679104000000000000\) | \([2]\) | \(7962624\) | \(2.8552\) |
Rank
sage: E.rank()
The elliptic curves in class 145600eu have rank \(2\).
Complex multiplication
The elliptic curves in class 145600eu do not have complex multiplication.Modular form 145600.2.a.eu
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
