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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 95760ea
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95760.cu4 | 95760ea1 | \([0, 0, 0, -1455123, 675611858]\) | \(114113060120923921/124104960\) | \(370575424880640\) | \([2]\) | \(1474560\) | \(2.0829\) | \(\Gamma_0(N)\)-optimal |
| 95760.cu3 | 95760ea2 | \([0, 0, 0, -1466643, 664370642]\) | \(116844823575501841/3760263939600\) | \(11228087959422566400\) | \([2, 2]\) | \(2949120\) | \(2.4295\) | |
| 95760.cu5 | 95760ea3 | \([0, 0, 0, 448557, 2275819922]\) | \(3342636501165359/751262567039460\) | \(-2243258004978754928640\) | \([2]\) | \(5898240\) | \(2.7761\) | |
| 95760.cu2 | 95760ea4 | \([0, 0, 0, -3566163, -1666516462]\) | \(1679731262160129361/570261564022500\) | \(1702791905986160640000\) | \([2, 2]\) | \(5898240\) | \(2.7761\) | |
| 95760.cu6 | 95760ea5 | \([0, 0, 0, 10469517, -11550442318]\) | \(42502666283088696719/43898058864843750\) | \(-131078901401481600000000\) | \([2]\) | \(11796480\) | \(3.1226\) | |
| 95760.cu1 | 95760ea6 | \([0, 0, 0, -51194163, -140959365262]\) | \(4969327007303723277361/1123462695162150\) | \(3354641632351057305600\) | \([2]\) | \(11796480\) | \(3.1226\) |
Rank
sage: E.rank()
The elliptic curves in class 95760ea have rank \(1\).
Complex multiplication
The elliptic curves in class 95760ea do not have complex multiplication.Modular form 95760.2.a.ea
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
