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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 208080.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
208080.m1 | 208080br4 | \([0, 0, 0, -272211123, -1728626305678]\) | \(30949975477232209/478125000\) | \(34460570029478400000000\) | \([2]\) | \(42467328\) | \(3.4596\) | |
208080.m2 | 208080br2 | \([0, 0, 0, -17521203, -25311058702]\) | \(8253429989329/936360000\) | \(67487580345730498560000\) | \([2, 2]\) | \(21233664\) | \(3.1130\) | |
208080.m3 | 208080br1 | \([0, 0, 0, -4204083, 2897264882]\) | \(114013572049/15667200\) | \(1129203958725948211200\) | \([2]\) | \(10616832\) | \(2.7664\) | \(\Gamma_0(N)\)-optimal |
208080.m4 | 208080br3 | \([0, 0, 0, 24094797, -127328521102]\) | \(21464092074671/109596256200\) | \(-7899083841566026203955200\) | \([2]\) | \(42467328\) | \(3.4596\) |
Rank
sage: E.rank()
The elliptic curves in class 208080.m have rank \(1\).
Complex multiplication
The elliptic curves in class 208080.m do not have complex multiplication.Modular form 208080.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.