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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 371280ew
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 371280.ew3 | 371280ew1 | \([0, 1, 0, -162776, -25331436]\) | \(116449478628435289/1996001280\) | \(8175621242880\) | \([2]\) | \(1769472\) | \(1.6070\) | \(\Gamma_0(N)\)-optimal |
| 371280.ew2 | 371280ew2 | \([0, 1, 0, -167896, -23658220]\) | \(127787213284071769/15197834433600\) | \(62250329840025600\) | \([2, 2]\) | \(3538944\) | \(1.9536\) | |
| 371280.ew1 | 371280ew3 | \([0, 1, 0, -657496, 180211220]\) | \(7674388308884766169/1007648705929320\) | \(4127329099486494720\) | \([2]\) | \(7077888\) | \(2.3001\) | |
| 371280.ew4 | 371280ew4 | \([0, 1, 0, 239784, -120359916]\) | \(372239584720800551/1745320379985000\) | \(-7148832276418560000\) | \([2]\) | \(7077888\) | \(2.3001\) |
Rank
sage: E.rank()
The elliptic curves in class 371280ew have rank \(1\).
Complex multiplication
The elliptic curves in class 371280ew do not have complex multiplication.Modular form 371280.2.a.ew
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.
