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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 152592.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152592.bh1 | 152592ch4 | \([0, -1, 0, -7335081352, -241797120368912]\) | \(441453577446719855661097/4354701912\) | \(430538415617359577088\) | \([2]\) | \(74317824\) | \(3.9911\) | |
| 152592.bh2 | 152592ch2 | \([0, -1, 0, -458453512, -3777776268560]\) | \(107784459654566688937/10704361149504\) | \(1058313239949607386218496\) | \([2, 2]\) | \(37158912\) | \(3.6445\) | |
| 152592.bh3 | 152592ch3 | \([0, -1, 0, -423865992, -4371851512080]\) | \(-85183593440646799657/34223681512621656\) | \(-3383609237278431611266105344\) | \([2]\) | \(74317824\) | \(3.9911\) | |
| 152592.bh4 | 152592ch1 | \([0, -1, 0, -30825992, -49548498192]\) | \(32765849647039657/8229948198912\) | \(813674260552352255705088\) | \([2]\) | \(18579456\) | \(3.2979\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152592.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 152592.bh do not have complex multiplication.Modular form 152592.2.a.bh
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.
