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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 486720.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
486720.g1 | 486720g3 | \([0, 0, 0, -20200908, -33543831152]\) | \(988345570681/44994560\) | \(41503772450210489303040\) | \([2]\) | \(55738368\) | \(3.1020\) | |
486720.g2 | 486720g1 | \([0, 0, 0, -3165708, 2155133968]\) | \(3803721481/26000\) | \(23982856676573184000\) | \([2]\) | \(18579456\) | \(2.5526\) | \(\Gamma_0(N)\)-optimal* |
486720.g3 | 486720g2 | \([0, 0, 0, -1218828, 4777191952]\) | \(-217081801/10562500\) | \(-9743035524857856000000\) | \([2]\) | \(37158912\) | \(2.8992\) | |
486720.g4 | 486720g4 | \([0, 0, 0, 10949172, -127654452848]\) | \(157376536199/7722894400\) | \(-7123733443211909765529600\) | \([2]\) | \(111476736\) | \(3.4485\) |
Rank
sage: E.rank()
The elliptic curves in class 486720.g have rank \(1\).
Complex multiplication
The elliptic curves in class 486720.g do not have complex multiplication.Modular form 486720.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.