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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 4900.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4900.i1 | 4900b1 | \([0, -1, 0, -24908, 1522312]\) | \(-177953104/125\) | \(-1200500000000\) | \([]\) | \(10368\) | \(1.2541\) | \(\Gamma_0(N)\)-optimal |
4900.i2 | 4900b2 | \([0, -1, 0, 24092, 6422312]\) | \(161017136/1953125\) | \(-18757812500000000\) | \([]\) | \(31104\) | \(1.8034\) |
Rank
sage: E.rank()
The elliptic curves in class 4900.i have rank \(0\).
Complex multiplication
The elliptic curves in class 4900.i do not have complex multiplication.Modular form 4900.2.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 LMFDB 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 LMFDB labels.