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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 182.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 182.c1 | 182a4 | \([1, -1, 1, -59134, 5547693]\) | \(22868021811807457713/8953460393696\) | \(8953460393696\) | \([2]\) | \(720\) | \(1.4500\) | |
| 182.c2 | 182a3 | \([1, -1, 1, -31294, -2081875]\) | \(3389174547561866673/74853681183008\) | \(74853681183008\) | \([2]\) | \(720\) | \(1.4500\) | |
| 182.c3 | 182a2 | \([1, -1, 1, -4254, 59693]\) | \(8511781274893233/3440817243136\) | \(3440817243136\) | \([2, 2]\) | \(360\) | \(1.1034\) | |
| 182.c4 | 182a1 | \([1, -1, 1, 866, 6445]\) | \(71903073502287/60782804992\) | \(-60782804992\) | \([4]\) | \(180\) | \(0.75686\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 182.c have rank \(0\).
Complex multiplication
The elliptic curves in class 182.c do not have complex multiplication.Modular form 182.2.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.
