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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 13872x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13872.q2 | 13872x1 | \([0, -1, 0, 91, 141]\) | \(4096/3\) | \(-60370944\) | \([]\) | \(3840\) | \(0.18130\) | \(\Gamma_0(N)\)-optimal |
13872.q1 | 13872x2 | \([0, -1, 0, -13509, 608877]\) | \(-13549359104/243\) | \(-4890046464\) | \([]\) | \(19200\) | \(0.98602\) |
Rank
sage: E.rank()
The elliptic curves in class 13872x have rank \(0\).
Complex multiplication
The elliptic curves in class 13872x do not have complex multiplication.Modular form 13872.2.a.x
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 Cremona 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 Cremona labels.