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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 15075e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15075.g2 | 15075e1 | \([0, 0, 1, 53700, -727844]\) | \(1503484706816/890163675\) | \(-10139520610546875\) | \([]\) | \(92160\) | \(1.7606\) | \(\Gamma_0(N)\)-optimal |
15075.g1 | 15075e2 | \([0, 0, 1, -675300, 235923781]\) | \(-2989967081734144/380653171875\) | \(-4335877535888671875\) | \([]\) | \(276480\) | \(2.3099\) |
Rank
sage: E.rank()
The elliptic curves in class 15075e have rank \(0\).
Complex multiplication
The elliptic curves in class 15075e do not have complex multiplication.Modular form 15075.2.a.e
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.