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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 310464.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.dn1 | 310464dn2 | \([0, 0, 0, -117516, -15503600]\) | \(5476248398/891\) | \(29201776902144\) | \([2]\) | \(1310720\) | \(1.5928\) | |
| 310464.dn2 | 310464dn1 | \([0, 0, 0, -6636, -290864]\) | \(-1972156/1089\) | \(-17845530329088\) | \([2]\) | \(655360\) | \(1.2462\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.dn do not have complex multiplication.Modular form 310464.2.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.
