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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 51600h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51600.bf1 | 51600h1 | \([0, -1, 0, -908, 9312]\) | \(20720464/3225\) | \(12900000000\) | \([2]\) | \(36864\) | \(0.66322\) | \(\Gamma_0(N)\)-optimal |
51600.bf2 | 51600h2 | \([0, -1, 0, 1592, 49312]\) | \(27871484/83205\) | \(-1331280000000\) | \([2]\) | \(73728\) | \(1.0098\) |
Rank
sage: E.rank()
The elliptic curves in class 51600h have rank \(0\).
Complex multiplication
The elliptic curves in class 51600h do not have complex multiplication.Modular form 51600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.