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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 176400g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.bx2 | 176400g1 | \([0, 0, 0, -1355340, 1010074975]\) | \(-1605176213504/1640558367\) | \(-281408654823368814000\) | \([2]\) | \(6193152\) | \(2.6193\) | \(\Gamma_0(N)\)-optimal |
| 176400.bx1 | 176400g2 | \([0, 0, 0, -25467015, 49450430050]\) | \(665567485783184/257298363\) | \(706159441093117536000\) | \([2]\) | \(12386304\) | \(2.9659\) |
Rank
sage: E.rank()
The elliptic curves in class 176400g have rank \(1\).
Complex multiplication
The elliptic curves in class 176400g do not have complex multiplication.Modular form 176400.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
