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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 7245p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7245.n3 | 7245p1 | \([1, -1, 0, -729, 6880]\) | \(58818484369/7455105\) | \(5434771545\) | \([2]\) | \(3840\) | \(0.59719\) | \(\Gamma_0(N)\)-optimal |
| 7245.n2 | 7245p2 | \([1, -1, 0, -2934, -53537]\) | \(3832302404449/472410225\) | \(344387054025\) | \([2, 2]\) | \(7680\) | \(0.94376\) | |
| 7245.n1 | 7245p3 | \([1, -1, 0, -45459, -3719192]\) | \(14251520160844849/264449745\) | \(192783864105\) | \([2]\) | \(15360\) | \(1.2903\) | |
| 7245.n4 | 7245p4 | \([1, -1, 0, 4311, -281030]\) | \(12152722588271/53476250625\) | \(-38984186705625\) | \([2]\) | \(15360\) | \(1.2903\) |
Rank
sage: E.rank()
The elliptic curves in class 7245p have rank \(0\).
Complex multiplication
The elliptic curves in class 7245p do not have complex multiplication.Modular form 7245.2.a.p
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
