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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 72450.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72450.f1 | 72450m2 | \([1, -1, 0, -1523382, 724085576]\) | \(158909194494247023/5080516\) | \(12499974553500\) | \([2]\) | \(884736\) | \(2.0155\) | |
| 72450.f2 | 72450m1 | \([1, -1, 0, -95082, 11363876]\) | \(-38638468208943/219395344\) | \(-539794819494000\) | \([2]\) | \(442368\) | \(1.6689\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72450.f have rank \(1\).
Complex multiplication
The elliptic curves in class 72450.f do not have complex multiplication.Modular form 72450.2.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.
