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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 146523.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
146523.e1 | 146523a2 | \([0, 1, 1, -142692, -20794588]\) | \(-13549359104/243\) | \(-5762529365931\) | \([]\) | \(1123200\) | \(1.5753\) | |
146523.e2 | 146523a1 | \([0, 1, 1, 958, -5560]\) | \(4096/3\) | \(-71142337851\) | \([]\) | \(224640\) | \(0.77063\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 146523.e have rank \(0\).
Complex multiplication
The elliptic curves in class 146523.e do not have complex multiplication.Modular form 146523.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.