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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 12882.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12882.h1 | 12882g2 | \([1, 0, 1, -8680, -159154]\) | \(72312097990757113/31003988313096\) | \(31003988313096\) | \([2]\) | \(41472\) | \(1.2852\) | |
12882.h2 | 12882g1 | \([1, 0, 1, -4160, 101198]\) | \(7958910549046393/151342682688\) | \(151342682688\) | \([2]\) | \(20736\) | \(0.93864\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12882.h have rank \(1\).
Complex multiplication
The elliptic curves in class 12882.h do not have complex multiplication.Modular form 12882.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.