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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 15456v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15456.o2 | 15456v1 | \([0, 1, 0, 6, 72]\) | \(314432/33327\) | \(-2132928\) | \([2]\) | \(1792\) | \(-0.10617\) | \(\Gamma_0(N)\)-optimal |
15456.o1 | 15456v2 | \([0, 1, 0, -224, 1176]\) | \(2438569736/91287\) | \(46738944\) | \([2]\) | \(3584\) | \(0.24040\) |
Rank
sage: E.rank()
The elliptic curves in class 15456v have rank \(1\).
Complex multiplication
The elliptic curves in class 15456v do not have complex multiplication.Modular form 15456.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.