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SageMath
E = EllipticCurve("jz1")
E.isogeny_class()
Elliptic curves in class 221760.jz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.jz1 | 221760ci1 | \([0, 0, 0, -80832, 18300256]\) | \(-4890195460096/9282994875\) | \(-110875496675328000\) | \([]\) | \(1990656\) | \(1.9604\) | \(\Gamma_0(N)\)-optimal |
| 221760.jz2 | 221760ci2 | \([0, 0, 0, 696768, -387762464]\) | \(3132137615458304/7250937873795\) | \(-86604737904583557120\) | \([]\) | \(5971968\) | \(2.5097\) |
Rank
sage: E.rank()
The elliptic curves in class 221760.jz have rank \(1\).
Complex multiplication
The elliptic curves in class 221760.jz do not have complex multiplication.Modular form 221760.2.a.jz
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
