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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 35904c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35904.u1 | 35904c1 | \([0, -1, 0, -4553, -102519]\) | \(2548895896000/333499353\) | \(1366013349888\) | \([2]\) | \(36864\) | \(1.0568\) | \(\Gamma_0(N)\)-optimal |
35904.u2 | 35904c2 | \([0, -1, 0, 7007, -548735]\) | \(1160935651000/4607830161\) | \(-150989378715648\) | \([2]\) | \(73728\) | \(1.4034\) |
Rank
sage: E.rank()
The elliptic curves in class 35904c have rank \(1\).
Complex multiplication
The elliptic curves in class 35904c do not have complex multiplication.Modular form 35904.2.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 Cremona 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 Cremona labels.