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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 816.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
816.c1 | 816a1 | \([0, -1, 0, -48, 144]\) | \(12194500/153\) | \(156672\) | \([2]\) | \(64\) | \(-0.19373\) | \(\Gamma_0(N)\)-optimal |
816.c2 | 816a2 | \([0, -1, 0, -8, 336]\) | \(-31250/23409\) | \(-47941632\) | \([2]\) | \(128\) | \(0.15284\) |
Rank
sage: E.rank()
The elliptic curves in class 816.c have rank \(1\).
Complex multiplication
The elliptic curves in class 816.c do not have complex multiplication.Modular form 816.2.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.