Show commands:
SageMath
E = EllipticCurve("hu1")
E.isogeny_class()
Elliptic curves in class 486720hu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 486720.hu4 | 486720hu1 | \([0, 0, 0, -13964808, -16934352968]\) | \(83587439220736/13990184325\) | \(50409342780245756236800\) | \([2]\) | \(33030144\) | \(3.0773\) | \(\Gamma_0(N)\)-optimal |
| 486720.hu2 | 486720hu2 | \([0, 0, 0, -213550428, -1201115753552]\) | \(18681746265374416/693005625\) | \(39952535049120245760000\) | \([2, 2]\) | \(66060288\) | \(3.4239\) | |
| 486720.hu3 | 486720hu3 | \([0, 0, 0, -203694348, -1316995657328]\) | \(-4053153720264484/903687890625\) | \(-208394395780904985600000000\) | \([2]\) | \(132120576\) | \(3.7705\) | |
| 486720.hu1 | 486720hu4 | \([0, 0, 0, -3416776428, -76872845487152]\) | \(19129597231400697604/26325\) | \(6070660596257587200\) | \([2]\) | \(132120576\) | \(3.7705\) |
Rank
sage: E.rank()
The elliptic curves in class 486720hu have rank \(1\).
Complex multiplication
The elliptic curves in class 486720hu do not have complex multiplication.Modular form 486720.2.a.hu
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.
