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SageMath
E = EllipticCurve("hg1")
E.isogeny_class()
Elliptic curves in class 142800hg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142800.fv4 | 142800hg1 | \([0, 1, 0, -17666108, -28851244212]\) | \(-152435594466395827792/1646846627220711\) | \(-6587386508882844000000\) | \([2]\) | \(8847360\) | \(3.0026\) | \(\Gamma_0(N)\)-optimal |
| 142800.fv3 | 142800hg2 | \([0, 1, 0, -283386608, -1836282085212]\) | \(157304700372188331121828/18069292138401\) | \(289108674214416000000\) | \([2, 2]\) | \(17694720\) | \(3.3492\) | |
| 142800.fv2 | 142800hg3 | \([0, 1, 0, -284115608, -1826360395212]\) | \(79260902459030376659234/842751810121431609\) | \(26968057923885811488000000\) | \([2]\) | \(35389440\) | \(3.6957\) | |
| 142800.fv1 | 142800hg4 | \([0, 1, 0, -4534185608, -117517526071212]\) | \(322159999717985454060440834/4250799\) | \(136025568000000\) | \([2]\) | \(35389440\) | \(3.6957\) |
Rank
sage: E.rank()
The elliptic curves in class 142800hg have rank \(0\).
Complex multiplication
The elliptic curves in class 142800hg do not have complex multiplication.Modular form 142800.2.a.hg
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.
