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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 57960c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57960.q1 | 57960c1 | \([0, 0, 0, -1067643, -424584442]\) | \(4867860927988386828/299954571875\) | \(8293144003200000\) | \([2]\) | \(675840\) | \(2.1143\) | \(\Gamma_0(N)\)-optimal |
57960.q2 | 57960c2 | \([0, 0, 0, -1004163, -477285538]\) | \(-2025082127708317494/607776572265625\) | \(-33607613340000000000\) | \([2]\) | \(1351680\) | \(2.4609\) |
Rank
sage: E.rank()
The elliptic curves in class 57960c have rank \(0\).
Complex multiplication
The elliptic curves in class 57960c do not have complex multiplication.Modular form 57960.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.