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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 217672.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 217672.f1 | 217672c2 | \([0, 1, 0, -2867648, 271560160]\) | \(263822189935250/149429406721\) | \(1477155236301994575872\) | \([2]\) | \(9031680\) | \(2.7520\) | |
| 217672.f2 | 217672c1 | \([0, 1, 0, 708392, 34111104]\) | \(7953970437500/4703287687\) | \(-23246716249293601792\) | \([2]\) | \(4515840\) | \(2.4054\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 217672.f have rank \(1\).
Complex multiplication
The elliptic curves in class 217672.f do not have complex multiplication.Modular form 217672.2.a.f
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.
