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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 26520.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26520.s1 | 26520e4 | \([0, 1, 0, -2348856, -92595600]\) | \(699782572199712476018/403188655517578125\) | \(825730366500000000000\) | \([2]\) | \(1327104\) | \(2.7031\) | |
26520.s2 | 26520e2 | \([0, 1, 0, -1557936, 745146864]\) | \(408387906477526456516/1765480810640625\) | \(1807852350096000000\) | \([2, 2]\) | \(663552\) | \(2.3566\) | |
26520.s3 | 26520e1 | \([0, 1, 0, -1556316, 746781120]\) | \(1628461040201585189584/30630848625\) | \(7841497248000\) | \([2]\) | \(331776\) | \(2.0100\) | \(\Gamma_0(N)\)-optimal |
26520.s4 | 26520e3 | \([0, 1, 0, -792936, 1478322864]\) | \(-26922086450129858258/445575877967449125\) | \(-912539398077335808000\) | \([2]\) | \(1327104\) | \(2.7031\) |
Rank
sage: E.rank()
The elliptic curves in class 26520.s have rank \(1\).
Complex multiplication
The elliptic curves in class 26520.s do not have complex multiplication.Modular form 26520.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.