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SageMath
E = EllipticCurve("ku1")
E.isogeny_class()
Elliptic curves in class 176400ku
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.sp1 | 176400ku1 | \([0, 0, 0, -100434075, 386571890250]\) | \(551105805571803/1376829440\) | \(279905944527175680000000\) | \([2]\) | \(30965760\) | \(3.3764\) | \(\Gamma_0(N)\)-optimal |
| 176400.sp2 | 176400ku2 | \([0, 0, 0, -62802075, 679762802250]\) | \(-134745327251163/903920796800\) | \(-183764812877665689600000000\) | \([2]\) | \(61931520\) | \(3.7230\) |
Rank
sage: E.rank()
The elliptic curves in class 176400ku have rank \(1\).
Complex multiplication
The elliptic curves in class 176400ku do not have complex multiplication.Modular form 176400.2.a.ku
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.
