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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 304200m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304200.m3 | 304200m1 | \([0, 0, 0, -76050, -7414875]\) | \(55296/5\) | \(4398429701250000\) | \([2]\) | \(1769472\) | \(1.7411\) | \(\Gamma_0(N)\)-optimal |
304200.m2 | 304200m2 | \([0, 0, 0, -266175, 44489250]\) | \(148176/25\) | \(351874376100000000\) | \([2, 2]\) | \(3538944\) | \(2.0877\) | |
304200.m1 | 304200m3 | \([0, 0, 0, -4068675, 3158736750]\) | \(132304644/5\) | \(281499500880000000\) | \([2]\) | \(7077888\) | \(2.4343\) | |
304200.m4 | 304200m4 | \([0, 0, 0, 494325, 252105750]\) | \(237276/625\) | \(-35187437610000000000\) | \([2]\) | \(7077888\) | \(2.4343\) |
Rank
sage: E.rank()
The elliptic curves in class 304200m have rank \(1\).
Complex multiplication
The elliptic curves in class 304200m do not have complex multiplication.Modular form 304200.2.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 Cremona 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 Cremona labels.