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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 277200.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.x1 | 277200x3 | \([0, 0, 0, -958005075, 11413000287250]\) | \(2084105208962185000201/31185000\) | \(1454967360000000000\) | \([2]\) | \(56623104\) | \(3.4887\) | |
| 277200.x2 | 277200x4 | \([0, 0, 0, -64917075, 146529855250]\) | \(648474704552553481/176469171805080\) | \(8233345679737812480000000\) | \([2]\) | \(56623104\) | \(3.4887\) | |
| 277200.x3 | 277200x2 | \([0, 0, 0, -59877075, 178317135250]\) | \(508859562767519881/62240270400\) | \(2903882055782400000000\) | \([2, 2]\) | \(28311552\) | \(3.1421\) | |
| 277200.x4 | 277200x1 | \([0, 0, 0, -3429075, 3271887250]\) | \(-95575628340361/43812679680\) | \(-2044124383150080000000\) | \([2]\) | \(14155776\) | \(2.7956\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.x have rank \(1\).
Complex multiplication
The elliptic curves in class 277200.x do not have complex multiplication.Modular form 277200.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
