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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 425880u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
425880.u3 | 425880u1 | \([0, 0, 0, -2456105223, -46850967803302]\) | \(1819018058610682173904/4844385\) | \(4363814270625788160\) | \([2]\) | \(115605504\) | \(3.6977\) | \(\Gamma_0(N)\)-optimal* |
425880.u2 | 425880u2 | \([0, 0, 0, -2456135643, -46849749232858]\) | \(454771411897393003396/23468066028225\) | \(84559985581622035101926400\) | \([2, 2]\) | \(231211008\) | \(4.0442\) | \(\Gamma_0(N)\)-optimal* |
425880.u1 | 425880u3 | \([0, 0, 0, -2590287843, -41446554734338]\) | \(266716694084614489298/51372277695070605\) | \(370208525573916982882806589440\) | \([2]\) | \(462422016\) | \(4.3908\) | \(\Gamma_0(N)\)-optimal* |
425880.u4 | 425880u4 | \([0, 0, 0, -2322470163, -52174955222962]\) | \(-192245661431796830258/51935513760073125\) | \(-374267422756018093050927360000\) | \([2]\) | \(462422016\) | \(4.3908\) |
Rank
sage: E.rank()
The elliptic curves in class 425880u have rank \(0\).
Complex multiplication
The elliptic curves in class 425880u do not have complex multiplication.Modular form 425880.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.