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SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 224400fj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.ch4 | 224400fj1 | \([0, -1, 0, -2666608, -1260020288]\) | \(32765849647039657/8229948198912\) | \(526716684730368000000\) | \([2]\) | \(8257536\) | \(2.6861\) | \(\Gamma_0(N)\)-optimal |
| 224400.ch2 | 224400fj2 | \([0, -1, 0, -39658608, -96107508288]\) | \(107784459654566688937/10704361149504\) | \(685079113568256000000\) | \([2, 2]\) | \(16515072\) | \(3.0326\) | |
| 224400.ch3 | 224400fj3 | \([0, -1, 0, -36666608, -111223092288]\) | \(-85183593440646799657/34223681512621656\) | \(-2190315616807785984000000\) | \([2]\) | \(33030144\) | \(3.3792\) | |
| 224400.ch1 | 224400fj4 | \([0, -1, 0, -634522608, -6151823028288]\) | \(441453577446719855661097/4354701912\) | \(278700922368000000\) | \([2]\) | \(33030144\) | \(3.3792\) |
Rank
sage: E.rank()
The elliptic curves in class 224400fj have rank \(1\).
Complex multiplication
The elliptic curves in class 224400fj do not have complex multiplication.Modular form 224400.2.a.fj
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.
