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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 277350dh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277350.dh2 | 277350dh1 | \([1, 0, 0, 7348812, -17130673008]\) | \(444369620591/1540767744\) | \(-152183629437698304000000\) | \([]\) | \(43464960\) | \(3.1313\) | \(\Gamma_0(N)\)-optimal |
277350.dh1 | 277350dh2 | \([1, 0, 0, -2768924688, 56087299131492]\) | \(-23769846831649063249/3261823333284\) | \(-322174523302929522233062500\) | \([]\) | \(304254720\) | \(4.1042\) |
Rank
sage: E.rank()
The elliptic curves in class 277350dh have rank \(0\).
Complex multiplication
The elliptic curves in class 277350dh do not have complex multiplication.Modular form 277350.2.a.dh
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.