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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 152460.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152460.e1 | 152460ba2 | \([0, 0, 0, -152823, -4842178]\) | \(1193895376/660275\) | \(218297347387257600\) | \([2]\) | \(1658880\) | \(2.0175\) | |
152460.e2 | 152460ba1 | \([0, 0, 0, -92928, 10838333]\) | \(4294967296/29645\) | \(612569087056080\) | \([2]\) | \(829440\) | \(1.6710\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152460.e have rank \(0\).
Complex multiplication
The elliptic curves in class 152460.e do not have complex multiplication.Modular form 152460.2.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 LMFDB 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 LMFDB labels.