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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 15030b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15030.e1 | 15030b1 | \([1, -1, 0, -24789, 1508445]\) | \(-62394574179743883/167000\) | \(-4509000\) | \([3]\) | \(17280\) | \(0.93707\) | \(\Gamma_0(N)\)-optimal |
15030.e2 | 15030b2 | \([1, -1, 0, -23964, 1612880]\) | \(-77325109990227/11923105280\) | \(-234682481226240\) | \([]\) | \(51840\) | \(1.4864\) |
Rank
sage: E.rank()
The elliptic curves in class 15030b have rank \(0\).
Complex multiplication
The elliptic curves in class 15030b do not have complex multiplication.Modular form 15030.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.