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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1170.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1170.h1 | 1170i4 | \([1, -1, 1, -35993, -2619269]\) | \(261984288445803/42250\) | \(831606750\) | \([2]\) | \(3456\) | \(1.1138\) | |
1170.h2 | 1170i3 | \([1, -1, 1, -2243, -40769]\) | \(-63378025803/812500\) | \(-15992437500\) | \([2]\) | \(1728\) | \(0.76723\) | |
1170.h3 | 1170i2 | \([1, -1, 1, -503, -2473]\) | \(520300455507/193072360\) | \(5212953720\) | \([6]\) | \(1152\) | \(0.56450\) | |
1170.h4 | 1170i1 | \([1, -1, 1, 97, -313]\) | \(3774555693/3515200\) | \(-94910400\) | \([6]\) | \(576\) | \(0.21793\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1170.h have rank \(1\).
Complex multiplication
The elliptic curves in class 1170.h do not have complex multiplication.Modular form 1170.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.