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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 3120v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3120.o2 | 3120v1 | \([0, 1, 0, 64, 564]\) | \(6967871/35100\) | \(-143769600\) | \([2]\) | \(1152\) | \(0.24753\) | \(\Gamma_0(N)\)-optimal |
3120.o1 | 3120v2 | \([0, 1, 0, -736, 6644]\) | \(10779215329/1232010\) | \(5046312960\) | \([2]\) | \(2304\) | \(0.59410\) |
Rank
sage: E.rank()
The elliptic curves in class 3120v have rank \(1\).
Complex multiplication
The elliptic curves in class 3120v do not have complex multiplication.Modular form 3120.2.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.