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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 142373f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142373.f1 | 142373f1 | \([0, -1, 1, -165177, -25783980]\) | \(-78843215872/539\) | \(-3407214683411\) | \([]\) | \(524160\) | \(1.5856\) | \(\Gamma_0(N)\)-optimal |
| 142373.f2 | 142373f2 | \([0, -1, 1, -91217, -48998175]\) | \(-13278380032/156590819\) | \(-989867417039247131\) | \([]\) | \(1572480\) | \(2.1349\) | |
| 142373.f3 | 142373f3 | \([0, -1, 1, 814793, 1268793370]\) | \(9463555063808/115539436859\) | \(-730366726862751223091\) | \([]\) | \(4717440\) | \(2.6842\) |
Rank
sage: E.rank()
The elliptic curves in class 142373f have rank \(0\).
Complex multiplication
The elliptic curves in class 142373f do not have complex multiplication.Modular form 142373.2.a.f
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
