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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 13860.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13860.j1 | 13860r1 | \([0, 0, 0, -20208, -2287532]\) | \(-4890195460096/9282994875\) | \(-1732429635552000\) | \([]\) | \(62208\) | \(1.6138\) | \(\Gamma_0(N)\)-optimal |
| 13860.j2 | 13860r2 | \([0, 0, 0, 174192, 48470308]\) | \(3132137615458304/7250937873795\) | \(-1353199029759118080\) | \([3]\) | \(186624\) | \(2.1631\) |
Rank
sage: E.rank()
The elliptic curves in class 13860.j have rank \(1\).
Complex multiplication
The elliptic curves in class 13860.j do not have complex multiplication.Modular form 13860.2.a.j
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.
