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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 18928.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18928.h1 | 18928h2 | \([0, 1, 0, -6816, 211732]\) | \(3543122/49\) | \(484379936768\) | \([2]\) | \(37632\) | \(1.0478\) | |
18928.h2 | 18928h1 | \([0, 1, 0, -56, 8932]\) | \(-4/7\) | \(-34598566912\) | \([2]\) | \(18816\) | \(0.70123\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18928.h have rank \(0\).
Complex multiplication
The elliptic curves in class 18928.h do not have complex multiplication.Modular form 18928.2.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.