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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 459186h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
459186.h2 | 459186h1 | \([1, 1, 0, 600457, -2023244139]\) | \(40251338884511/2997011332224\) | \(-1782692233708113995904\) | \([]\) | \(26968032\) | \(2.7572\) | \(\Gamma_0(N)\)-optimal |
459186.h1 | 459186h2 | \([1, 1, 0, -3090251153, -66122191120209]\) | \(-5486773802537974663600129/2635437714\) | \(-1567619813330128194\) | \([]\) | \(188776224\) | \(3.7302\) |
Rank
sage: E.rank()
The elliptic curves in class 459186h have rank \(0\).
Complex multiplication
The elliptic curves in class 459186h do not have complex multiplication.Modular form 459186.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.