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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 60984z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60984.f4 | 60984z1 | \([0, 0, 0, -7986, 1782209]\) | \(-2725888/64827\) | \(-1339551904421808\) | \([2]\) | \(276480\) | \(1.5833\) | \(\Gamma_0(N)\)-optimal |
| 60984.f3 | 60984z2 | \([0, 0, 0, -274791, 55196570]\) | \(6940769488/35721\) | \(11809926994086144\) | \([2, 2]\) | \(552960\) | \(1.9299\) | |
| 60984.f2 | 60984z3 | \([0, 0, 0, -427251, -12892066]\) | \(6522128932/3720087\) | \(4919678159250742272\) | \([2]\) | \(1105920\) | \(2.2764\) | |
| 60984.f1 | 60984z4 | \([0, 0, 0, -4391211, 3541804310]\) | \(7080974546692/189\) | \(249945544848384\) | \([2]\) | \(1105920\) | \(2.2764\) |
Rank
sage: E.rank()
The elliptic curves in class 60984z have rank \(1\).
Complex multiplication
The elliptic curves in class 60984z do not have complex multiplication.Modular form 60984.2.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.
