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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 425880f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 425880.f2 | 425880f1 | \([0, 0, 0, -137163, 18810038]\) | \(174011157652/7503125\) | \(12305513001600000\) | \([2]\) | \(2949120\) | \(1.8512\) | \(\Gamma_0(N)\)-optimal |
| 425880.f1 | 425880f2 | \([0, 0, 0, -366483, -60488818]\) | \(1659578027546/478515625\) | \(1569580740000000000\) | \([2]\) | \(5898240\) | \(2.1978\) |
Rank
sage: E.rank()
The elliptic curves in class 425880f have rank \(1\).
Complex multiplication
The elliptic curves in class 425880f do not have complex multiplication.Modular form 425880.2.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 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.
