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SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 154560.gh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.gh1 | 154560m4 | \([0, 1, 0, -274785, -55533537]\) | \(8753151307882969/65205\) | \(17093099520\) | \([2]\) | \(720896\) | \(1.5581\) | |
| 154560.gh2 | 154560m2 | \([0, 1, 0, -17185, -870817]\) | \(2141202151369/5832225\) | \(1528882790400\) | \([2, 2]\) | \(360448\) | \(1.2115\) | |
| 154560.gh3 | 154560m3 | \([0, 1, 0, -10465, -1552225]\) | \(-483551781049/3672913125\) | \(-962832138240000\) | \([2]\) | \(720896\) | \(1.5581\) | |
| 154560.gh4 | 154560m1 | \([0, 1, 0, -1505, -2145]\) | \(1439069689/828345\) | \(217145671680\) | \([2]\) | \(180224\) | \(0.86491\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 154560.gh have rank \(0\).
Complex multiplication
The elliptic curves in class 154560.gh do not have complex multiplication.Modular form 154560.2.a.gh
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.
