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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 7098.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7098.p1 | 7098p1 | \([1, 0, 1, -11782, -493192]\) | \(-82318551880501/54432\) | \(-119587104\) | \([]\) | \(12000\) | \(0.86692\) | \(\Gamma_0(N)\)-optimal |
7098.p2 | 7098p2 | \([1, 0, 1, 24293, -2543578]\) | \(721710134999099/1691848015872\) | \(-3716990090870784\) | \([]\) | \(60000\) | \(1.6716\) |
Rank
sage: E.rank()
The elliptic curves in class 7098.p have rank \(0\).
Complex multiplication
The elliptic curves in class 7098.p do not have complex multiplication.Modular form 7098.2.a.p
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.