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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 16800.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16800.m1 | 16800bj2 | \([0, -1, 0, -1639408, -807355688]\) | \(60910917333827912/3255076125\) | \(26040609000000000\) | \([2]\) | \(221184\) | \(2.2173\) | |
16800.m2 | 16800bj3 | \([0, -1, 0, -530033, 138659937]\) | \(257307998572864/19456203375\) | \(1245197016000000000\) | \([4]\) | \(221184\) | \(2.2173\) | |
16800.m3 | 16800bj1 | \([0, -1, 0, -108158, -11105688]\) | \(139927692143296/27348890625\) | \(27348890625000000\) | \([2, 2]\) | \(110592\) | \(1.8707\) | \(\Gamma_0(N)\)-optimal |
16800.m4 | 16800bj4 | \([0, -1, 0, 222592, -66010188]\) | \(152461584507448/322998046875\) | \(-2583984375000000000\) | \([2]\) | \(221184\) | \(2.2173\) |
Rank
sage: E.rank()
The elliptic curves in class 16800.m have rank \(1\).
Complex multiplication
The elliptic curves in class 16800.m do not have complex multiplication.Modular form 16800.2.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.