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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 16830.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16830.w1 | 16830o4 | \([1, -1, 0, -51904464, -143918301952]\) | \(785681552361835673854227/2604236800\) | \(51259192934400\) | \([2]\) | \(967680\) | \(2.7367\) | |
| 16830.w2 | 16830o3 | \([1, -1, 0, -3243984, -2248180480]\) | \(-191808834096148160787/11043434659840\) | \(-217367924409630720\) | \([2]\) | \(483840\) | \(2.3901\) | |
| 16830.w3 | 16830o2 | \([1, -1, 0, -643089, -195791427]\) | \(1089365384367428097483/16063552169500000\) | \(433715908576500000\) | \([6]\) | \(322560\) | \(2.1874\) | |
| 16830.w4 | 16830o1 | \([1, -1, 0, -4209, -8344035]\) | \(-305460292990923/1114070936704000\) | \(-30079915291008000\) | \([6]\) | \(161280\) | \(1.8408\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16830.w have rank \(0\).
Complex multiplication
The elliptic curves in class 16830.w do not have complex multiplication.Modular form 16830.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
