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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 308763i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308763.i2 | 308763i1 | \([0, 0, 1, -224094, -4705425]\) | \(2092859392/1195061\) | \(710664170982187149\) | \([]\) | \(3953664\) | \(2.1152\) | \(\Gamma_0(N)\)-optimal |
308763.i1 | 308763i2 | \([0, 0, 1, -11692434, 15388673940]\) | \(297278942052352/3411821\) | \(2028899731900393989\) | \([3]\) | \(11860992\) | \(2.6645\) |
Rank
sage: E.rank()
The elliptic curves in class 308763i have rank \(1\).
Complex multiplication
The elliptic curves in class 308763i do not have complex multiplication.Modular form 308763.2.a.i
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.