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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 9702.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9702.m1 | 9702i4 | \([1, -1, 0, -451887, 117033965]\) | \(4406910829875/7744\) | \(17932666707648\) | \([2]\) | \(69120\) | \(1.8023\) | |
| 9702.m2 | 9702i3 | \([1, -1, 0, -28527, 1795373]\) | \(1108717875/45056\) | \(104335515389952\) | \([2]\) | \(34560\) | \(1.4557\) | |
| 9702.m3 | 9702i2 | \([1, -1, 0, -7212, 60724]\) | \(13060888875/7086244\) | \(22509617049612\) | \([2]\) | \(23040\) | \(1.2530\) | |
| 9702.m4 | 9702i1 | \([1, -1, 0, -4272, -105680]\) | \(2714704875/21296\) | \(67647233808\) | \([2]\) | \(11520\) | \(0.90644\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.m have rank \(1\).
Complex multiplication
The elliptic curves in class 9702.m do not have complex multiplication.Modular form 9702.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
