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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 290145g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
290145.g4 | 290145g1 | \([1, 1, 1, 383899, 57796274]\) | \(10519294081031/8500170375\) | \(-5056099571523315375\) | \([2]\) | \(6720000\) | \(2.2768\) | \(\Gamma_0(N)\)-optimal |
290145.g3 | 290145g2 | \([1, 1, 1, -1840546, 500905718]\) | \(1159246431432649/488076890625\) | \(290319516984916265625\) | \([2, 2]\) | \(13440000\) | \(2.6233\) | |
290145.g1 | 290145g3 | \([1, 1, 1, -25342291, 49074312284]\) | \(3026030815665395929/1364501953125\) | \(811637583268798828125\) | \([2]\) | \(26880000\) | \(2.9699\) | |
290145.g2 | 290145g4 | \([1, 1, 1, -13929921, -19669007532]\) | \(502552788401502649/10024505152875\) | \(5962809446414720197875\) | \([2]\) | \(26880000\) | \(2.9699\) |
Rank
sage: E.rank()
The elliptic curves in class 290145g have rank \(1\).
Complex multiplication
The elliptic curves in class 290145g do not have complex multiplication.Modular form 290145.2.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 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.