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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 35904cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35904.j2 | 35904cd1 | \([0, -1, 0, -26354369, 50062566753]\) | \(7722211175253055152433/340131399900069888\) | \(89163405695403920719872\) | \([2]\) | \(3115008\) | \(3.1668\) | \(\Gamma_0(N)\)-optimal |
35904.j1 | 35904cd2 | \([0, -1, 0, -70918849, -163838024351]\) | \(150476552140919246594353/42832838728685592576\) | \(11228371675692555980242944\) | \([2]\) | \(6230016\) | \(3.5134\) |
Rank
sage: E.rank()
The elliptic curves in class 35904cd have rank \(0\).
Complex multiplication
The elliptic curves in class 35904cd do not have complex multiplication.Modular form 35904.2.a.cd
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.