Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 100905.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100905.s1 | 100905g4 | \([1, 1, 0, -108132, 13640151]\) | \(157551496201/13125\) | \(11648485813125\) | \([2]\) | \(483840\) | \(1.5510\) | |
| 100905.s2 | 100905g2 | \([1, 1, 0, -7227, 179424]\) | \(47045881/11025\) | \(9784728083025\) | \([2, 2]\) | \(241920\) | \(1.2045\) | |
| 100905.s3 | 100905g1 | \([1, 1, 0, -2422, -44489]\) | \(1771561/105\) | \(93187886505\) | \([2]\) | \(120960\) | \(0.85788\) | \(\Gamma_0(N)\)-optimal |
| 100905.s4 | 100905g3 | \([1, 1, 0, 16798, 1145229]\) | \(590589719/972405\) | \(-863013016922805\) | \([2]\) | \(483840\) | \(1.5510\) |
Rank
sage: E.rank()
The elliptic curves in class 100905.s have rank \(0\).
Complex multiplication
The elliptic curves in class 100905.s do not have complex multiplication.Modular form 100905.2.a.s
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.
