Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 141120z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.lm4 | 141120z1 | \([0, 0, 0, 6468, 93296]\) | \(21296/15\) | \(-21077881896960\) | \([2]\) | \(294912\) | \(1.2451\) | \(\Gamma_0(N)\)-optimal |
| 141120.lm3 | 141120z2 | \([0, 0, 0, -28812, 784784]\) | \(470596/225\) | \(1264672913817600\) | \([2, 2]\) | \(589824\) | \(1.5917\) | |
| 141120.lm1 | 141120z3 | \([0, 0, 0, -381612, 90678224]\) | \(546718898/405\) | \(4552822489743360\) | \([2]\) | \(1179648\) | \(1.9382\) | |
| 141120.lm2 | 141120z4 | \([0, 0, 0, -240492, -44853424]\) | \(136835858/1875\) | \(21077881896960000\) | \([2]\) | \(1179648\) | \(1.9382\) |
Rank
sage: E.rank()
The elliptic curves in class 141120z have rank \(1\).
Complex multiplication
The elliptic curves in class 141120z do not have complex multiplication.Modular form 141120.2.a.z
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 Cremona 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 Cremona labels.
