Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 35280.dj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.dj1 | 35280dp1 | \([0, 0, 0, -36156267, -83499528294]\) | \(551105805571803/1376829440\) | \(13059291747859908526080\) | \([2]\) | \(3870720\) | \(3.1210\) | \(\Gamma_0(N)\)-optimal |
| 35280.dj2 | 35280dp2 | \([0, 0, 0, -22608747, -146828765286]\) | \(-134745327251163/903920796800\) | \(-8573731109620370413977600\) | \([2]\) | \(7741440\) | \(3.4676\) |
Rank
sage: E.rank()
The elliptic curves in class 35280.dj have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.dj do not have complex multiplication.Modular form 35280.2.a.dj
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
