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SageMath
E = EllipticCurve("ib1")
E.isogeny_class()
Elliptic curves in class 176400ib
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.qx2 | 176400ib1 | \([0, 0, 0, 84525, -11600750]\) | \(596183/864\) | \(-96786192384000000\) | \([]\) | \(1244160\) | \(1.9448\) | \(\Gamma_0(N)\)-optimal |
| 176400.qx1 | 176400ib2 | \([0, 0, 0, -2561475, -1585970750]\) | \(-16591834777/98304\) | \(-11012117889024000000\) | \([]\) | \(3732480\) | \(2.4941\) |
Rank
sage: E.rank()
The elliptic curves in class 176400ib have rank \(1\).
Complex multiplication
The elliptic curves in class 176400ib do not have complex multiplication.Modular form 176400.2.a.ib
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.
