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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 96600.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96600.c1 | 96600t2 | \([0, -1, 0, -73288, 7660972]\) | \(170054560416634/1633023\) | \(418053888000\) | \([2]\) | \(251904\) | \(1.3916\) | |
96600.c2 | 96600t1 | \([0, -1, 0, -4688, 114972]\) | \(89036727188/8117781\) | \(1039075968000\) | \([2]\) | \(125952\) | \(1.0450\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96600.c have rank \(0\).
Complex multiplication
The elliptic curves in class 96600.c do not have complex multiplication.Modular form 96600.2.a.c
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.