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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 7200h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7200.u3 | 7200h1 | \([0, 0, 0, -1425, -7000]\) | \(438976/225\) | \(164025000000\) | \([2, 2]\) | \(6144\) | \(0.84418\) | \(\Gamma_0(N)\)-optimal |
| 7200.u1 | 7200h2 | \([0, 0, 0, -18300, -952000]\) | \(14526784/15\) | \(699840000000\) | \([2]\) | \(12288\) | \(1.1908\) | |
| 7200.u2 | 7200h3 | \([0, 0, 0, -12675, 544250]\) | \(38614472/405\) | \(2361960000000\) | \([2]\) | \(12288\) | \(1.1908\) | |
| 7200.u4 | 7200h4 | \([0, 0, 0, 5325, -54250]\) | \(2863288/1875\) | \(-10935000000000\) | \([2]\) | \(12288\) | \(1.1908\) |
Rank
sage: E.rank()
The elliptic curves in class 7200h have rank \(0\).
Complex multiplication
The elliptic curves in class 7200h do not have complex multiplication.Modular form 7200.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
