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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 265200.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 265200.f1 | 265200f3 | \([0, -1, 0, -735808, 243180112]\) | \(2753580869496292/39328497\) | \(629255952000000\) | \([2]\) | \(2621440\) | \(1.9791\) | |
| 265200.f2 | 265200f2 | \([0, -1, 0, -47308, 3582112]\) | \(2927363579728/320445801\) | \(1281783204000000\) | \([2, 2]\) | \(1310720\) | \(1.6325\) | |
| 265200.f3 | 265200f1 | \([0, -1, 0, -11183, -391638]\) | \(618724784128/87947613\) | \(21986903250000\) | \([2]\) | \(655360\) | \(1.2859\) | \(\Gamma_0(N)\)-optimal |
| 265200.f4 | 265200f4 | \([0, -1, 0, 63192, 17726112]\) | \(1744147297148/9513325341\) | \(-152213205456000000\) | \([2]\) | \(2621440\) | \(1.9791\) |
Rank
sage: E.rank()
The elliptic curves in class 265200.f have rank \(1\).
Complex multiplication
The elliptic curves in class 265200.f do not have complex multiplication.Modular form 265200.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
