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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 3146.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3146.a1 | 3146i2 | \([1, -1, 0, -25735, 1749919]\) | \(-1064019559329/125497034\) | \(-222325651050074\) | \([]\) | \(19600\) | \(1.4887\) | |
3146.a2 | 3146i1 | \([1, -1, 0, -325, -3371]\) | \(-2146689/1664\) | \(-2947877504\) | \([]\) | \(2800\) | \(0.51579\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3146.a have rank \(1\).
Complex multiplication
The elliptic curves in class 3146.a do not have complex multiplication.Modular form 3146.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.