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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 840.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
840.h1 | 840d3 | \([0, 1, 0, -202616, 34012320]\) | \(898353183174324196/29899176238575\) | \(30616756468300800\) | \([4]\) | \(7680\) | \(1.9362\) | |
840.h2 | 840d2 | \([0, 1, 0, -31116, -1385280]\) | \(13015144447800784/4341909875625\) | \(1111528928160000\) | \([2, 2]\) | \(3840\) | \(1.5897\) | |
840.h3 | 840d1 | \([0, 1, 0, -27991, -1811530]\) | \(151591373397612544/32558203125\) | \(520931250000\) | \([2]\) | \(1920\) | \(1.2431\) | \(\Gamma_0(N)\)-optimal |
840.h4 | 840d4 | \([0, 1, 0, 90384, -9452880]\) | \(79743193254623804/84085819746075\) | \(-86103879419980800\) | \([2]\) | \(7680\) | \(1.9362\) |
Rank
sage: E.rank()
The elliptic curves in class 840.h have rank \(0\).
Complex multiplication
The elliptic curves in class 840.h do not have complex multiplication.Modular form 840.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.