Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 102960.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.f1 | 102960dn4 | \([0, 0, 0, -46803, 3782738]\) | \(3797146126801/127239255\) | \(379934379601920\) | \([2]\) | \(393216\) | \(1.5702\) | |
| 102960.f2 | 102960dn2 | \([0, 0, 0, -7203, -153502]\) | \(13841287201/4601025\) | \(13738587033600\) | \([2, 2]\) | \(196608\) | \(1.2236\) | |
| 102960.f3 | 102960dn1 | \([0, 0, 0, -6483, -200878]\) | \(10091699281/2145\) | \(6404935680\) | \([2]\) | \(98304\) | \(0.87707\) | \(\Gamma_0(N)\)-optimal |
| 102960.f4 | 102960dn3 | \([0, 0, 0, 20877, -1057678]\) | \(337008232079/356874375\) | \(-1065621173760000\) | \([2]\) | \(393216\) | \(1.5702\) |
Rank
sage: E.rank()
The elliptic curves in class 102960.f have rank \(2\).
Complex multiplication
The elliptic curves in class 102960.f do not have complex multiplication.Modular form 102960.2.a.f
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.
