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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4840.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4840.c1 | 4840f1 | \([0, 0, 0, -4598, 115797]\) | \(379275264/15125\) | \(428717762000\) | \([2]\) | \(5760\) | \(0.99852\) | \(\Gamma_0(N)\)-optimal |
4840.c2 | 4840f2 | \([0, 0, 0, 2057, 423258]\) | \(2122416/171875\) | \(-77948684000000\) | \([2]\) | \(11520\) | \(1.3451\) |
Rank
sage: E.rank()
The elliptic curves in class 4840.c have rank \(1\).
Complex multiplication
The elliptic curves in class 4840.c do not have complex multiplication.Modular form 4840.2.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.