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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 92400.dp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.dp1 | 92400fp2 | \([0, -1, 0, -18830768, 11770084032]\) | \(1442307535559216746181/717904548395249292\) | \(367567128778367637504000\) | \([2]\) | \(8429568\) | \(3.2147\) | |
| 92400.dp2 | 92400fp1 | \([0, -1, 0, -15331568, 23093495232]\) | \(778419129671687951621/693260592493392\) | \(354949423356616704000\) | \([2]\) | \(4214784\) | \(2.8681\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.dp have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.dp do not have complex multiplication.Modular form 92400.2.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.
