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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 880.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
880.h1 | 880i3 | \([0, 0, 0, -947, -11214]\) | \(22930509321/6875\) | \(28160000\) | \([2]\) | \(256\) | \(0.40748\) | |
880.h2 | 880i4 | \([0, 0, 0, -467, 3794]\) | \(2749884201/73205\) | \(299847680\) | \([4]\) | \(256\) | \(0.40748\) | |
880.h3 | 880i2 | \([0, 0, 0, -67, -126]\) | \(8120601/3025\) | \(12390400\) | \([2, 2]\) | \(128\) | \(0.060908\) | |
880.h4 | 880i1 | \([0, 0, 0, 13, -14]\) | \(59319/55\) | \(-225280\) | \([2]\) | \(64\) | \(-0.28567\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 880.h have rank \(0\).
Complex multiplication
The elliptic curves in class 880.h do not have complex multiplication.Modular form 880.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.