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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 11270.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11270.s1 | 11270p3 | \([1, 1, 1, -82860, 9066665]\) | \(534774372149809/5323062500\) | \(626252980062500\) | \([2]\) | \(82944\) | \(1.6579\) | |
| 11270.s2 | 11270p4 | \([1, 1, 1, -21610, 22247665]\) | \(-9486391169809/1813439640250\) | \(-213349360235772250\) | \([2]\) | \(165888\) | \(2.0044\) | |
| 11270.s3 | 11270p1 | \([1, 1, 1, -7400, -240983]\) | \(380920459249/12622400\) | \(1485012737600\) | \([2]\) | \(27648\) | \(1.1086\) | \(\Gamma_0(N)\)-optimal |
| 11270.s4 | 11270p2 | \([1, 1, 1, 2400, -821143]\) | \(12994449551/2489452840\) | \(-292881637173160\) | \([2]\) | \(55296\) | \(1.4551\) |
Rank
sage: E.rank()
The elliptic curves in class 11270.s have rank \(0\).
Complex multiplication
The elliptic curves in class 11270.s do not have complex multiplication.Modular form 11270.2.a.s
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 LMFDB 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 LMFDB labels.
