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SageMath
E = EllipticCurve("hs1")
E.isogeny_class()
Elliptic curves in class 377520hs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.hs4 | 377520hs1 | \([0, 1, 0, -2460, 165900]\) | \(-3631696/24375\) | \(-11054540640000\) | \([2]\) | \(983040\) | \(1.1862\) | \(\Gamma_0(N)\)-optimal |
| 377520.hs3 | 377520hs2 | \([0, 1, 0, -62960, 6046500]\) | \(15214885924/38025\) | \(68980333593600\) | \([2, 2]\) | \(1966080\) | \(1.5328\) | |
| 377520.hs1 | 377520hs3 | \([0, 1, 0, -1006760, 388474260]\) | \(31103978031362/195\) | \(707490600960\) | \([2]\) | \(3932160\) | \(1.8793\) | |
| 377520.hs2 | 377520hs4 | \([0, 1, 0, -87160, 945140]\) | \(20183398562/11567205\) | \(41967634958346240\) | \([2]\) | \(3932160\) | \(1.8793\) |
Rank
sage: E.rank()
The elliptic curves in class 377520hs have rank \(0\).
Complex multiplication
The elliptic curves in class 377520hs do not have complex multiplication.Modular form 377520.2.a.hs
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
