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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 288990fh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 288990.fh4 | 288990fh1 | \([1, -1, 1, -2889932, -1975599921]\) | \(-758575480593601/40535043840\) | \(-142632432613861482240\) | \([2]\) | \(14745600\) | \(2.6261\) | \(\Gamma_0(N)\)-optimal |
| 288990.fh3 | 288990fh2 | \([1, -1, 1, -46816412, -123282967089]\) | \(3225005357698077121/8526675600\) | \(30003186569570931600\) | \([2, 2]\) | \(29491200\) | \(2.9727\) | |
| 288990.fh2 | 288990fh3 | \([1, -1, 1, -47394392, -120082345041]\) | \(3345930611358906241/165622259047500\) | \(582782290706116427647500\) | \([2]\) | \(58982400\) | \(3.3193\) | |
| 288990.fh1 | 288990fh4 | \([1, -1, 1, -749062112, -7890682205649]\) | \(13209596798923694545921/92340\) | \(324920798890740\) | \([2]\) | \(58982400\) | \(3.3193\) |
Rank
sage: E.rank()
The elliptic curves in class 288990fh have rank \(0\).
Complex multiplication
The elliptic curves in class 288990fh do not have complex multiplication.Modular form 288990.2.a.fh
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.
