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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 485100j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485100.j2 | 485100j1 | \([0, 0, 0, -5350800, 3962850500]\) | \(1007878144/179685\) | \(3020533548569460000000\) | \([]\) | \(20901888\) | \(2.8410\) | \(\Gamma_0(N)\)-optimal* |
485100.j1 | 485100j2 | \([0, 0, 0, -412834800, 3228587484500]\) | \(462893166690304/4125\) | \(69341908828500000000\) | \([]\) | \(62705664\) | \(3.3903\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485100j have rank \(1\).
Complex multiplication
The elliptic curves in class 485100j do not have complex multiplication.Modular form 485100.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.