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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 810.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
810.h1 | 810g1 | \([1, -1, 1, -4388, 112967]\) | \(-115330920751809/4096000\) | \(-331776000\) | \([3]\) | \(1080\) | \(0.72441\) | \(\Gamma_0(N)\)-optimal |
810.h2 | 810g2 | \([1, -1, 1, -1028, 277831]\) | \(-225866529/62500000\) | \(-33215062500000\) | \([]\) | \(3240\) | \(1.2737\) |
Rank
sage: E.rank()
The elliptic curves in class 810.h have rank \(0\).
Complex multiplication
The elliptic curves in class 810.h do not have complex multiplication.Modular form 810.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.