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SageMath
E = EllipticCurve("gt1")
E.isogeny_class()
Elliptic curves in class 176400.gt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.gt1 | 176400ju2 | \([0, 0, 0, -66675, -4740750]\) | \(55306341/15625\) | \(9261000000000000\) | \([2]\) | \(1179648\) | \(1.7706\) | |
| 176400.gt2 | 176400ju1 | \([0, 0, 0, -24675, 1433250]\) | \(2803221/125\) | \(74088000000000\) | \([2]\) | \(589824\) | \(1.4240\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.gt have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.gt do not have complex multiplication.Modular form 176400.2.a.gt
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.
