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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 435c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 435.d3 | 435c1 | \([1, 0, 1, -28, 53]\) | \(2305199161/1305\) | \(1305\) | \([2]\) | \(48\) | \(-0.45550\) | \(\Gamma_0(N)\)-optimal |
| 435.d2 | 435c2 | \([1, 0, 1, -33, 31]\) | \(3803721481/1703025\) | \(1703025\) | \([2, 2]\) | \(96\) | \(-0.10892\) | |
| 435.d1 | 435c3 | \([1, 0, 1, -258, -1589]\) | \(1888690601881/31827645\) | \(31827645\) | \([2]\) | \(192\) | \(0.23765\) | |
| 435.d4 | 435c4 | \([1, 0, 1, 112, 263]\) | \(157376536199/118918125\) | \(-118918125\) | \([4]\) | \(192\) | \(0.23765\) |
Rank
sage: E.rank()
The elliptic curves in class 435c have rank \(0\).
Complex multiplication
The elliptic curves in class 435c do not have complex multiplication.Modular form 435.2.a.c
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.
