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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 397800.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.j1 | 397800j3 | \([0, 0, 0, -459012675, 3785167736750]\) | \(916959671620739147236/2731145625\) | \(31856082570000000000\) | \([2]\) | \(75497472\) | \(3.3957\) | |
| 397800.j2 | 397800j2 | \([0, 0, 0, -28700175, 59091799250]\) | \(896581610757188944/1545359765625\) | \(4506269076562500000000\) | \([2, 2]\) | \(37748736\) | \(3.0491\) | |
| 397800.j3 | 397800j4 | \([0, 0, 0, -19749675, 96621245750]\) | \(-73039208963041156/303497314453125\) | \(-3539992675781250000000000\) | \([2]\) | \(75497472\) | \(3.3957\) | |
| 397800.j4 | 397800j1 | \([0, 0, 0, -2365050, 285465125]\) | \(8027441608013824/4452347908125\) | \(811440406255781250000\) | \([2]\) | \(18874368\) | \(2.7025\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 397800.j have rank \(0\).
Complex multiplication
The elliptic curves in class 397800.j do not have complex multiplication.Modular form 397800.2.a.j
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 LMFDB 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 LMFDB labels.
