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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 304200f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304200.f2 | 304200f1 | \([0, 0, 0, 177450, -91999375]\) | \(702464/4563\) | \(-4014006945360750000\) | \([2]\) | \(5160960\) | \(2.2515\) | \(\Gamma_0(N)\)-optimal |
304200.f1 | 304200f2 | \([0, 0, 0, -2294175, -1216588750]\) | \(94875856/9477\) | \(133388538491988000000\) | \([2]\) | \(10321920\) | \(2.5980\) |
Rank
sage: E.rank()
The elliptic curves in class 304200f have rank \(2\).
Complex multiplication
The elliptic curves in class 304200f do not have complex multiplication.Modular form 304200.2.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.