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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 35520d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35520.q4 | 35520d1 | \([0, -1, 0, -556, 2350]\) | \(297542483776/140562075\) | \(8995972800\) | \([2]\) | \(25600\) | \(0.60415\) | \(\Gamma_0(N)\)-optimal |
| 35520.q2 | 35520d2 | \([0, -1, 0, -7401, 247401]\) | \(10946963145664/7700625\) | \(31541760000\) | \([2, 2]\) | \(51200\) | \(0.95072\) | |
| 35520.q3 | 35520d3 | \([0, -1, 0, -5921, 347745]\) | \(-700700304968/1170703125\) | \(-38361600000000\) | \([2]\) | \(102400\) | \(1.2973\) | |
| 35520.q1 | 35520d4 | \([0, -1, 0, -118401, 15720801]\) | \(5602005828691208/2775\) | \(90931200\) | \([2]\) | \(102400\) | \(1.2973\) |
Rank
sage: E.rank()
The elliptic curves in class 35520d have rank \(1\).
Complex multiplication
The elliptic curves in class 35520d do not have complex multiplication.Modular form 35520.2.a.d
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.
