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SageMath
E = EllipticCurve("hb1")
E.isogeny_class()
Elliptic curves in class 369600hb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.hb1 | 369600hb1 | \([0, -1, 0, -224533, -84648563]\) | \(-4890195460096/9282994875\) | \(-2376446688000000000\) | \([]\) | \(5971968\) | \(2.2158\) | \(\Gamma_0(N)\)-optimal |
| 369600.hb2 | 369600hb2 | \([0, -1, 0, 1935467, 1794551437]\) | \(3132137615458304/7250937873795\) | \(-1856240095691520000000\) | \([]\) | \(17915904\) | \(2.7651\) |
Rank
sage: E.rank()
The elliptic curves in class 369600hb have rank \(1\).
Complex multiplication
The elliptic curves in class 369600hb do not have complex multiplication.Modular form 369600.2.a.hb
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.
