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SageMath
E = EllipticCurve("up1")
E.isogeny_class()
Elliptic curves in class 235200up
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.up2 | 235200up1 | \([0, 1, 0, -157208, 28213338]\) | \(-29218112/6561\) | \(-96486886125000000\) | \([2]\) | \(2211840\) | \(1.9792\) | \(\Gamma_0(N)\)-optimal |
235200.up1 | 235200up2 | \([0, 1, 0, -2637833, 1648061463]\) | \(2156689088/81\) | \(76236552000000000\) | \([2]\) | \(4423680\) | \(2.3258\) |
Rank
sage: E.rank()
The elliptic curves in class 235200up have rank \(1\).
Complex multiplication
The elliptic curves in class 235200up do not have complex multiplication.Modular form 235200.2.a.up
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.