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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 123840fl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123840.w2 | 123840fl1 | \([0, 0, 0, -12031428, 14910079552]\) | \(64504166108617130176/5165826416015625\) | \(15425075025000000000000\) | \([2]\) | \(7225344\) | \(3.0008\) | \(\Gamma_0(N)\)-optimal |
123840.w1 | 123840fl2 | \([0, 0, 0, -40156428, -80613670448]\) | \(299786086083570891272/55964100325078125\) | \(1336863265160624640000000\) | \([2]\) | \(14450688\) | \(3.3474\) |
Rank
sage: E.rank()
The elliptic curves in class 123840fl have rank \(2\).
Complex multiplication
The elliptic curves in class 123840fl do not have complex multiplication.Modular form 123840.2.a.fl
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.