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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 4950j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4950.c2 | 4950j1 | \([1, -1, 0, 8208, -45824]\) | \(3355354844375/1987172352\) | \(-36216216115200\) | \([]\) | \(12672\) | \(1.2911\) | \(\Gamma_0(N)\)-optimal |
4950.c1 | 4950j2 | \([1, -1, 0, -103167, 14116621]\) | \(-6663170841705625/850403524608\) | \(-15498604235980800\) | \([]\) | \(38016\) | \(1.8404\) |
Rank
sage: E.rank()
The elliptic curves in class 4950j have rank \(0\).
Complex multiplication
The elliptic curves in class 4950j do not have complex multiplication.Modular form 4950.2.a.j
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.