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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 259920du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.du4 | 259920du1 | \([0, 0, 0, 191118093, 6103488653746]\) | \(5495662324535111/117739817533440\) | \(-16539883278919721998362869760\) | \([2]\) | \(154828800\) | \(4.0949\) | \(\Gamma_0(N)\)-optimal |
| 259920.du3 | 259920du2 | \([0, 0, 0, -4067411187, 94572731034034]\) | \(52974743974734147769/3152005008998400\) | \(442788141136680533710444953600\) | \([2, 2]\) | \(309657600\) | \(4.4415\) | |
| 259920.du1 | 259920du3 | \([0, 0, 0, -64119327987, 6249281673482674]\) | \(207530301091125281552569/805586668007040\) | \(113167403678929401121312604160\) | \([2]\) | \(619315200\) | \(4.7881\) | |
| 259920.du2 | 259920du4 | \([0, 0, 0, -12151962867, -398104699076174]\) | \(1412712966892699019449/330160465517040000\) | \(46380363732215586286071644160000\) | \([2]\) | \(619315200\) | \(4.7881\) |
Rank
sage: E.rank()
The elliptic curves in class 259920du have rank \(1\).
Complex multiplication
The elliptic curves in class 259920du do not have complex multiplication.Modular form 259920.2.a.du
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.
