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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 361920.dp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361920.dp1 | 361920dp1 | \([0, 1, 0, -53281, -4044961]\) | \(63812982460681/10201800960\) | \(2674340910858240\) | \([2]\) | \(1474560\) | \(1.6826\) | \(\Gamma_0(N)\)-optimal |
| 361920.dp2 | 361920dp2 | \([0, 1, 0, 95199, -22426785]\) | \(363979050334199/1041836936400\) | \(-273111301855641600\) | \([2]\) | \(2949120\) | \(2.0292\) |
Rank
sage: E.rank()
The elliptic curves in class 361920.dp have rank \(1\).
Complex multiplication
The elliptic curves in class 361920.dp do not have complex multiplication.Modular form 361920.2.a.dp
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.
