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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 2400.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2400.z1 | 2400ba2 | \([0, 1, 0, -4008, -99012]\) | \(890277128/15\) | \(120000000\) | \([2]\) | \(1536\) | \(0.68052\) | |
2400.z2 | 2400ba3 | \([0, 1, 0, -1008, 10488]\) | \(14172488/1875\) | \(15000000000\) | \([2]\) | \(1536\) | \(0.68052\) | |
2400.z3 | 2400ba1 | \([0, 1, 0, -258, -1512]\) | \(1906624/225\) | \(225000000\) | \([2, 2]\) | \(768\) | \(0.33395\) | \(\Gamma_0(N)\)-optimal |
2400.z4 | 2400ba4 | \([0, 1, 0, 367, -7137]\) | \(85184/405\) | \(-25920000000\) | \([4]\) | \(1536\) | \(0.68052\) |
Rank
sage: E.rank()
The elliptic curves in class 2400.z have rank \(1\).
Complex multiplication
The elliptic curves in class 2400.z do not have complex multiplication.Modular form 2400.2.a.z
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.