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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 24255.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24255.m1 | 24255bx4 | \([1, -1, 1, -253582727, 1554337501476]\) | \(21026497979043461623321/161783881875\) | \(13875575988740956875\) | \([2]\) | \(2949120\) | \(3.2655\) | |
| 24255.m2 | 24255bx2 | \([1, -1, 1, -15859472, 24255542994]\) | \(5143681768032498601/14238434358225\) | \(1221175284018082695225\) | \([2, 2]\) | \(1474560\) | \(2.9190\) | |
| 24255.m3 | 24255bx3 | \([1, -1, 1, -9608297, 43566672804]\) | \(-1143792273008057401/8897444448004035\) | \(-763099297118292274298235\) | \([2]\) | \(2949120\) | \(3.2655\) | |
| 24255.m4 | 24255bx1 | \([1, -1, 1, -1392467, 43563426]\) | \(3481467828171481/2005331497785\) | \(171989503884139541985\) | \([2]\) | \(737280\) | \(2.5724\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24255.m have rank \(1\).
Complex multiplication
The elliptic curves in class 24255.m do not have complex multiplication.Modular form 24255.2.a.m
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.
