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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 35904.dd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35904.dd1 | 35904cw2 | \([0, 1, 0, -78497, 4862175]\) | \(204055591784617/78708537864\) | \(20632970949820416\) | \([2]\) | \(258048\) | \(1.8295\) | |
35904.dd2 | 35904cw1 | \([0, 1, 0, -34977, -2475297]\) | \(18052771191337/444958272\) | \(116643141255168\) | \([2]\) | \(129024\) | \(1.4829\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35904.dd have rank \(0\).
Complex multiplication
The elliptic curves in class 35904.dd do not have complex multiplication.Modular form 35904.2.a.dd
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.