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SageMath
E = EllipticCurve("ma1")
E.isogeny_class()
Elliptic curves in class 100800.ma
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.ma1 | 100800my4 | \([0, 0, 0, -3362700, -2373446000]\) | \(5633270409316/14175\) | \(10581580800000000\) | \([2]\) | \(1572864\) | \(2.3131\) | |
100800.ma2 | 100800my3 | \([0, 0, 0, -590700, 127906000]\) | \(30534944836/8203125\) | \(6123600000000000000\) | \([2]\) | \(1572864\) | \(2.3131\) | |
100800.ma3 | 100800my2 | \([0, 0, 0, -212700, -36146000]\) | \(5702413264/275625\) | \(51438240000000000\) | \([2, 2]\) | \(786432\) | \(1.9665\) | |
100800.ma4 | 100800my1 | \([0, 0, 0, 7800, -2189000]\) | \(4499456/180075\) | \(-2100394800000000\) | \([2]\) | \(393216\) | \(1.6199\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.ma have rank \(0\).
Complex multiplication
The elliptic curves in class 100800.ma do not have complex multiplication.Modular form 100800.2.a.ma
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.