Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 12480.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12480.u1 | 12480bv2 | \([0, -1, 0, -54561, 4923585]\) | \(68523370149961/243360\) | \(63795363840\) | \([2]\) | \(30720\) | \(1.2916\) | |
| 12480.u2 | 12480bv1 | \([0, -1, 0, -3361, 80065]\) | \(-16022066761/998400\) | \(-261724569600\) | \([2]\) | \(15360\) | \(0.94498\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12480.u have rank \(1\).
Complex multiplication
The elliptic curves in class 12480.u do not have complex multiplication.Modular form 12480.2.a.u
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.
