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SageMath
E = EllipticCurve("hd1")
E.isogeny_class()
Elliptic curves in class 176400hd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.w2 | 176400hd1 | \([0, 0, 0, 437325, 7803250]\) | \(34391/20\) | \(-5379251109120000000\) | \([]\) | \(2903040\) | \(2.2835\) | \(\Gamma_0(N)\)-optimal |
| 176400.w1 | 176400hd2 | \([0, 0, 0, -5736675, -5740190750]\) | \(-77626969/8000\) | \(-2151700443648000000000\) | \([]\) | \(8709120\) | \(2.8328\) |
Rank
sage: E.rank()
The elliptic curves in class 176400hd have rank \(1\).
Complex multiplication
The elliptic curves in class 176400hd do not have complex multiplication.Modular form 176400.2.a.hd
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
