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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 271440.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271440.v1 | 271440v1 | \([0, 0, 0, -119883, 13591802]\) | \(63812982460681/10201800960\) | \(30462414437744640\) | \([2]\) | \(1474560\) | \(1.8853\) | \(\Gamma_0(N)\)-optimal |
271440.v2 | 271440v2 | \([0, 0, 0, 214197, 75797498]\) | \(363979050334199/1041836936400\) | \(-3110908422699417600\) | \([2]\) | \(2949120\) | \(2.2319\) |
Rank
sage: E.rank()
The elliptic curves in class 271440.v have rank \(0\).
Complex multiplication
The elliptic curves in class 271440.v do not have complex multiplication.Modular form 271440.2.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 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.