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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 310464.dz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.dz1 | 310464dz3 | \([0, 0, 0, -1129369836, -10358298308176]\) | \(14171198121996897746/4077720290568771\) | \(45839843569837850284168445952\) | \([2]\) | \(283115520\) | \(4.2060\) | |
| 310464.dz2 | 310464dz2 | \([0, 0, 0, -1035454476, -12823050582160]\) | \(21843440425782779332/3100814593569\) | \(17428961010031308036440064\) | \([2, 2]\) | \(141557760\) | \(3.8594\) | |
| 310464.dz3 | 310464dz1 | \([0, 0, 0, -1035419196, -12823968186736]\) | \(87364831012240243408/1760913\) | \(2474421082988101632\) | \([2]\) | \(70778880\) | \(3.5128\) | \(\Gamma_0(N)\)-optimal |
| 310464.dz4 | 310464dz4 | \([0, 0, 0, -942103596, -15229076163280]\) | \(-8226100326647904626/4152140742401883\) | \(-46676443833548108989181853696\) | \([2]\) | \(283115520\) | \(4.2060\) |
Rank
sage: E.rank()
The elliptic curves in class 310464.dz have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.dz do not have complex multiplication.Modular form 310464.2.a.dz
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
