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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 355740.dn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
355740.dn1 | 355740dn1 | \([0, 1, 0, -3351861, 2360798460]\) | \(1248870793216/42525\) | \(141810587412555600\) | \([2]\) | \(8064000\) | \(2.3828\) | \(\Gamma_0(N)\)-optimal |
355740.dn2 | 355740dn2 | \([0, 1, 0, -3203636, 2579222820]\) | \(-68150496976/14467005\) | \(-771903389404022641920\) | \([2]\) | \(16128000\) | \(2.7294\) |
Rank
sage: E.rank()
The elliptic curves in class 355740.dn have rank \(1\).
Complex multiplication
The elliptic curves in class 355740.dn do not have complex multiplication.Modular form 355740.2.a.dn
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.