Show commands:
SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 35280.dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.dm1 | 35280cq6 | \([0, 0, 0, -4621827, 3824361506]\) | \(62161150998242/1607445\) | \(282346132215490560\) | \([2]\) | \(786432\) | \(2.4552\) | |
| 35280.dm2 | 35280cq4 | \([0, 0, 0, -300027, 54887546]\) | \(34008619684/4862025\) | \(427004953041945600\) | \([2, 2]\) | \(393216\) | \(2.1086\) | |
| 35280.dm3 | 35280cq2 | \([0, 0, 0, -79527, -7778554]\) | \(2533446736/275625\) | \(6051657497760000\) | \([2, 2]\) | \(196608\) | \(1.7620\) | |
| 35280.dm4 | 35280cq1 | \([0, 0, 0, -77322, -8275561]\) | \(37256083456/525\) | \(720435416400\) | \([2]\) | \(98304\) | \(1.4155\) | \(\Gamma_0(N)\)-optimal |
| 35280.dm5 | 35280cq3 | \([0, 0, 0, 105693, -38636206]\) | \(1486779836/8203125\) | \(-720435416400000000\) | \([4]\) | \(393216\) | \(2.1086\) | |
| 35280.dm6 | 35280cq5 | \([0, 0, 0, 493773, 296043986]\) | \(75798394558/259416045\) | \(-45566172989053839360\) | \([2]\) | \(786432\) | \(2.4552\) |
Rank
sage: E.rank()
The elliptic curves in class 35280.dm have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.dm do not have complex multiplication.Modular form 35280.2.a.dm
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
