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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 11088.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11088.m1 | 11088ca4 | \([0, 0, 0, -5795571, 5370224690]\) | \(7209828390823479793/49509306\) | \(147833995567104\) | \([2]\) | \(147456\) | \(2.3187\) | |
11088.m2 | 11088ca3 | \([0, 0, 0, -505011, 11749106]\) | \(4770223741048753/2740574865798\) | \(8183312700074975232\) | \([2]\) | \(147456\) | \(2.3187\) | |
11088.m3 | 11088ca2 | \([0, 0, 0, -362451, 83798930]\) | \(1763535241378513/4612311396\) | \(13772288031473664\) | \([2, 2]\) | \(73728\) | \(1.9721\) | |
11088.m4 | 11088ca1 | \([0, 0, 0, -13971, 2324306]\) | \(-100999381393/723148272\) | \(-2159309169819648\) | \([2]\) | \(36864\) | \(1.6255\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11088.m have rank \(1\).
Complex multiplication
The elliptic curves in class 11088.m do not have complex multiplication.Modular form 11088.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.