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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 7956.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7956.a1 | 7956b2 | \([0, 0, 0, -22071, -1262050]\) | \(6371214852688/77571\) | \(14476610304\) | \([2]\) | \(13824\) | \(1.0980\) | |
7956.a2 | 7956b1 | \([0, 0, 0, -1416, -18619]\) | \(26919436288/2738853\) | \(31945981392\) | \([2]\) | \(6912\) | \(0.75143\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7956.a have rank \(1\).
Complex multiplication
The elliptic curves in class 7956.a do not have complex multiplication.Modular form 7956.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.