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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1872.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1872.c1 | 1872r4 | \([0, 0, 0, -2986491, 1986506026]\) | \(986551739719628473/111045168\) | \(331579094925312\) | \([4]\) | \(30720\) | \(2.2105\) | |
| 1872.c2 | 1872r3 | \([0, 0, 0, -336891, -25526486]\) | \(1416134368422073/725251155408\) | \(2165588346029801472\) | \([2]\) | \(30720\) | \(2.2105\) | |
| 1872.c3 | 1872r2 | \([0, 0, 0, -187131, 30873130]\) | \(242702053576633/2554695936\) | \(7628281189761024\) | \([2, 2]\) | \(15360\) | \(1.8640\) | |
| 1872.c4 | 1872r1 | \([0, 0, 0, -2811, 1197610]\) | \(-822656953/207028224\) | \(-618182964412416\) | \([2]\) | \(7680\) | \(1.5174\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1872.c have rank \(0\).
Complex multiplication
The elliptic curves in class 1872.c do not have complex multiplication.Modular form 1872.2.a.c
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.
